Learn Hardcore Turkish: Şahsen ben bu çözümü tercih ederim; daha hızlı çalışıyor. - Personally, I prefer this solution; it works faster.

Şahsen means personally; ben is I. Either alone is fine; using both adds emphasis.
All are correct with slight differences in emphasis: Şahsen bu çözümü tercih ederim. / Ben bu çözümü tercih ederim. / Bu çözümü tercih ederim.

Why is it bu çözümü (with -ü) instead of bu çözüm?

The accusative suffix -(y)I marks a definite direct object. Bu çözüm is definite, so it becomes bu çözüm-ü.
Tercih etmek is transitive and normally takes an accusative object when it’s specific/definite.

Should it be çözümünü instead of çözümü?

No. Çözüm-ünü means its solution (possessive), which adds an owner.
Çözüm-ü is just the definite object the solution. Use çözümünü only if you mean the solution of it.

Can I just say Bunu tercih ederim?

Yes. Bunu is this (object pronoun). It’s perfectly natural if the referent is clear.
Bu çözümü makes it explicit that the this is a solution.

What’s the difference between tercih ederim and tercih ediyorum?

Ederim (aorist) = general, settled or polite preference, often like I’d prefer.
Ediyorum (present continuous) = current, immediate preference or ongoing choice in this context.

Why is it ederim and not something like eterim?

The verb is etmek. Before vowel-initial suffixes, the stem et- surfaces as ed-: ederim, ediyorum (but ettim in past).
This is a regular stem alternation with etmek (similar to gitmek → gidiyorum).

Why use çalışıyor instead of çalışır?

Çalışıyor (present continuous) suggests an observed/known current fact: it is running/operating faster (now/as tested).
Çalışır (aorist) states a general property or rule: it runs faster (as a general truth). Both are possible; nuance differs.

Who is the subject of çalışıyor? There’s no o or bu çözüm there.

It’s omitted but understood: third-person singular referring back to bu çözüm.
You could say Bu çözüm daha hızlı çalışıyor for clarity, but Turkish commonly drops the subject when clear.

Is the semicolon appropriate? Could I use a comma or a connector?

The semicolon neatly links two closely related clauses.
You could also use a comma plus çünkü: …, çünkü daha hızlı çalışıyor. or a reason clause: … daha hızlı çalıştığı için tercih ederim.

Do I need hızlıca to make it an adverb? Why is hızlı used before a verb?

In Turkish, adjectives often serve as adverbs without extra morphology. Daha hızlı çalışıyor is standard.
Hızlıca exists but is less common here; it can sound stylistically different and often describes how someone works rather than performance speed.

Could I say daha hızlı çalışır or daha hızlıdır?

Daha hızlı çalışır = general/habitual faster performance; fully fine.
Daha hızlıdır makes faster the predicate adjective of a noun phrase (e.g., Bu çözüm daha hızlıdır.). It’s more formal and drops the idea of working/operating unless context implies it.

How does vowel harmony give -ü in çözümü?

Can I replace bu with şu or o?

Is a comma after Şahsen required: Şahsen, ben…?

Optional. Many writers insert a comma after sentence-initial adverbs for rhythm/clarity, but it’s not mandatory.

Can I drop ben?

Yes. The verb ending -im already shows first person singular. Şahsen bu çözümü tercih ederim is fully natural.
Keeping ben adds emphasis or contrast (I, personally).

Are other word orders possible?

Yes, with nuance:
- Ben şahsen bu çözümü tercih ederim. (stronger I emphasis)
- Bu çözümü şahsen tercih ederim. (focus on the object, with personally modifying the act)
- Keep the object near tercih ederim for clarity.

Is çalışmak the right verb here? What about işe yaramak?

Çalışmak = to work/run/operate (machines, programs, methods in a technical sense).
İşe yaramak = to be effective/useful. Use it if you mean the solution is effective, not that it operates faster.

How would I say prefer doing X rather than Y?

Use the verbal noun with -(y)I and tercih etmek:
- X yapmayı Y yapmaya tercih ederim.
- With objects: Bu çözümü şuna tercih ederim.