Learn Hardcore Turkish: Ben bu odada sessizce çalışabilmek istiyorum. - I want to be able to work quietly in this room.

Using -ebil- adds the idea of possibility / ability / being allowed. It often implies something is making it difficult and you wish you could:

Bu odada sessizce çalışmak istiyorum.
= I want to work/study quietly in this room. (simple wish)
Bu odada sessizce çalışabilmek istiyorum.
= I want to be able to work/study quietly in this room. (if only I could; I’m not really able to now)

Both are grammatically correct; -ebil- just adds that nuance of having the chance / freedom.

What exactly does the suffix -ebil- / -abil- mean, and how is it used?

-ebil- / -abil- is a verb suffix of ability/possibility, similar to English “can / be able to / may”.

Form:
verb stem + (y)ebil / (y)abil

Choice of e / a depends on vowel harmony; b sometimes attaches directly, sometimes via -y-.

Meaning:

gelmek – to come
gelebilmek – to be able to come / can come
yazmak – to write
yazabilmek – to be able to write
anlamak – to understand
anlayabilmek – to be able to understand

With tense and person:

Gelebilirim. – I can come.
Yazabildin mi? – Were you able to write (it)?

In your sentence:

çalış-a-bil-mek – to be able to work/study
çalışabilmek istiyorum – I want to be able to work/study

Why isn’t there a separate word for “to” (as in “want to work”) before çalışabilmek?

In Turkish, the English “to” of “to verb” is built into the verb itself with the infinitive suffix -mek / -mak.

çalışmak = to work / to study
çalışabilmek = to be able to work / study

So:

istemek = to want
çalışabilmek istiyorum = I want to be able to work/study
(literally: I want the being-able-to-work/study)

Other examples:

Gitmek istiyorum. – I want to go.
Yemek istiyorum. – I want to eat.
Türkçe öğrenmek istiyorum. – I want to learn Turkish.

No extra word like English “to” is needed; -mek / -mak already does that job.

Why is istiyorum at the very end of the sentence? Can I put it earlier?

Turkish is typically S–O–V (Subject–Object–Verb). The conjugated main verb usually comes last.

In your sentence:

Ben (subject – I)
bu odada (location – in this room)
sessizce (manner – quietly)
çalışabilmek (infinitive: to be able to work/study)
istiyorum (main verb: I want)

So the normal order is:

Ben bu odada sessizce çalışabilmek istiyorum.

If you move istiyorum away from the end, it usually sounds unnatural or wrong:

✗ Ben istiyorum bu odada sessizce çalışabilmek. → feels un-Turkish.
✓ Ben bu odada sessizce çalışabilmek istiyorum.

You can sometimes move things around for emphasis, but the finite verb (here istiyorum) almost always stays at the end:

Bu odada sessizce çalışabilmek istiyorum ben.
(extra emphasis on ben – me, as opposed to someone else)

Do I really need to say Ben, since -um in istiyorum already means “I”?

You don’t need Ben. The ending -um in istiyorum already shows that the subject is “I”.

İstiyorum. – I want.
Bu odada sessizce çalışabilmek istiyorum. – I want to be able to work quietly in this room.

So:

Ben bu odada sessizce çalışabilmek istiyorum.
Bu odada sessizce çalışabilmek istiyorum.

Both are correct. Ben is used mainly for emphasis or contrast:

Ben bu odada sessizce çalışabilmek istiyorum, onlar konuşmak istiyor.
I want to be able to work quietly in this room, (but) they want to chat.

In neutral sentences, it’s very common to omit subject pronouns in Turkish.

Why is it bu odada and not just bu oda?

Bu oda means “this room”.

To say “in this room / inside this room”, you need the locative case suffix -da / -de / -ta / -te:

bu oda – this room
bu odada – in this room

So:

Bu odada oturuyorum. – I am sitting in this room.
Bu odada kimse yok. – There is nobody in this room.
Bu odada sessizce çalışabilmek istiyorum. – I want to be able to work quietly in this room.

How do I know whether to use -da, -de, -ta, or -te (like in odada)?

They are all forms of the same locative case (“in / on / at”). Which one you use depends on:

Vowel harmony (a vs e)
Voiced vs voiceless final consonant
Vowel harmony
Look at the last vowel of the noun:

If it’s a back vowel (a, ı, o, u) → use -da / -ta
If it’s a front vowel (e, i, ö, ü) → use -de / -te

Voiced / voiceless consonant
Look at the last sound of the noun:

Ends in a vowel or voiced consonant (b, c, d, g, ğ, j, l, m, n, r, v, y, z) → use d (-da / -de)
Ends in a voiceless consonant (p, ç, t, k, f, s, h, ş) → use t (-ta / -te)

Examples:

oda (o–d–a) → last vowel a (back), ends with a (vowel) → odada (in the room)
ev (e–v) → last vowel e (front), ends with v (voiced) → evde (at home)
park → last vowel a (back), ends with k (voiceless) → parkta (in the park)
şehir → last vowel i (front), ends with r (voiced) → şehirde (in the city)

So bu oda → bu odada (in this room).

What is sessizce exactly, and how is it different from sessiz?

sessiz = quiet (adjective)
sessizce = quietly / in a quiet way (adverb)

Sessizce is formed with the adverbial suffix -ce / -ca added to an adjective:

yavaş → yavaşça – slowly
dikkatli → dikkatlice – carefully
sessiz → sessizce – quietly

In your sentence, sessizce modifies the verb çalışabilmek:

sessizce çalışabilmek – to be able to work quietly

You can also say:

sessiz çalışmak – to work in silence / to work quietly

In many cases, sessiz çalışmak and sessizce çalışmak are very close in meaning.
Sessizce explicitly marks manner (“in a quiet way”), while sessiz can feel slightly more like “in silence”, but in everyday speech both are used to mean “quietly”.

Could I say Ben bu odada sessizce çalışmak istiyorum instead? How does that change the meaning?

Yes, that sentence is grammatically correct:

Ben bu odada sessizce çalışmak istiyorum.
= I want to work quietly in this room.

Difference in nuance:

çalışmak istiyorum – I want to work/study. (simple desire)
çalışabilmek istiyorum – I want to be able to work/study. (I wish I could; something is preventing me)

Examples of when çalışabilmek feels more natural:

Others are making noise, and you’re frustrated:
Bu odada sessizce çalışabilmek istiyorum ama herkes konuşuyor.
I want to be able to work quietly in this room, but everyone is talking.

If you just mean “I want to (quietly) study in this room” as a neutral statement, çalışmak istiyorum is enough.

Why do we use istiyorum (present continuous) and not isterim?

Both come from istemek = to want, but they have different aspects/uses.

istiyorum = present continuous
→ “I want (now / currently).”
Used for current, actual desires.
isterim = aorist (general/habitual / sometimes “would like”)
→ “I (generally) want / I would want / I’d like.”
Used for general preferences, conditionals, or a polite tone.

Your sentence:

Ben bu odada sessizce çalışabilmek istiyorum.
= I want (right now / in this situation) to be able to work quietly in this room.

Some contrast:

Genelde sessiz yerlerde çalışmayı isterim.
I (generally) prefer / would like to work in quiet places. (habitual preference)
In a shop/restaurant:
Bir çay isterim. – I’d like a tea. (polite / slightly formal)

For an immediate, specific wish (as in your sentence), istiyorum is the natural choice.

Can I move sessizce or bu odada to other positions in the sentence?

Yes, Turkish allows some flexibility in word order, especially with adverbs, but the main verb still stays at the end.

Neutral and most natural:

Ben bu odada sessizce çalışabilmek istiyorum.

Other acceptable variants (changing emphasis a bit):

Bu odada sessizce çalışabilmek istiyorum.
(no Ben; completely natural)
Ben sessizce bu odada çalışabilmek istiyorum.
(slightly unusual but understandable; more focus on “quietly in this room” as a chunk)
Ben bu odada çalışabilmek istiyorum sessizce.
(sounds odd; putting sessizce at the very end is not typical here)

General rule:

Keep the finite verb (istiyorum) at the very end.
Elements before it (Ben / bu odada / sessizce / çalışabilmek) can move somewhat, but changing the order too much can sound marked or unnatural.