Learn Hardcore Finnish: Tämä kahvi on vahva mutta herkullinen.

tämä = this (near me)
tuo = that (a bit further away / near you)
se = that / it (often used for things that are already known in the context, not so much about physical distance)

In your sentence, Tämä kahvi literally means “this coffee (here)”, e.g. the cup you’re holding.

Compare:

Tämä kahvi on vahva. – This coffee (right here) is strong.
Se kahvi on vahva. – That coffee / The coffee is strong. (already known or mentioned)
Tuo kahvi on vahva. – That coffee (over there) is strong. (physically further away)

Why is there no word for “the” or “a” in Tämä kahvi on vahva mutta herkullinen?

Finnish has no articles like English a / an / the.

Definiteness or indefiniteness is shown by:

context
demonstrative words like tämä (this), se (that / it), yksi (one), etc.
sometimes word order

So kahvi on its own can mean “coffee”, “the coffee”, or “a coffee” depending on context.

Here, Tämä kahvi already specifies which coffee we mean (this one), so English naturally translates it as “this coffee” without needing a separate article word in Finnish.

What is the role of on in this sentence?

On is the 3rd person singular present tense of the verb olla (to be). It corresponds to English “is”.

Minä olen – I am
Sinä olet – You are
Hän on – He/She is
Kahvi on – Coffee is

In Tämä kahvi on vahva mutta herkullinen, on links the subject (Tämä kahvi) to the adjectives (vahva, herkullinen) in exactly the same way is does in English: “This coffee is strong but delicious.”

Why is kahvi (not kahvia) used here?

Kahvi is in the nominative singular, the basic dictionary form, used for the subject of the sentence.

With olla (to be), Finnish can use nominative or partitive to describe something, depending on nuance:

Kahvi on vahva. – The coffee is strong. (thinking of the coffee as a specific item/portion)
Kahvi on vahvaa. – Coffee is strong. (more like a substance, an indefinite mass)

In your sentence, Tämä kahvi on vahva..., the speaker is probably thinking of this particular cup as a unit, so kahvi (nominative) fits very naturally. Treat it almost like saying “This cup of coffee is strong …” in English.

Why are the adjectives vahva and herkullinen in this form and not changed for case?

Here vahva and herkullinen are predicate adjectives: they describe the subject after the verb on.

Predicate adjectives in Finnish usually agree with the subject in:

number (singular/plural)
case (often nominative in simple “X is Y” statements)

Since Tämä kahvi is nominative singular:

vahva (nominative singular)
herkullinen (nominative singular)

If the subject were plural, they would change:

Nämä kahvit ovat vahvoja mutta herkullisia.
These coffees are strong but delicious.

Here vahvoja and herkullisia are plural forms agreeing with kahvit.

Could I also say “Tämä kahvi on vahvaa mutta herkullista”? Is that correct?

Yes, that is grammatically correct, and it sounds natural. The nuance changes slightly:

Tämä kahvi on vahva mutta herkullinen.
– Treats kahvi more like a discrete item (this particular coffee / cup), so adjectives are in nominative.
Tämä kahvi on vahvaa mutta herkullista.
– Treats kahvi more like a substance or an indefinite amount, so the adjectives are in the partitive.

In everyday speech both patterns occur. Many learners are taught first the nominative pattern “X on hyvä / vahva / kallis”, but you will also hear and use the partitive pattern with mass nouns like kahvi, vesi, viini, etc.

What does mutta mean, and how is it different from vaan?

Mutta means “but” in the general contrastive sense, just like in English.

Tämä kahvi on vahva, mutta herkullinen.
This coffee is strong, but (nevertheless) delicious.

Vaan is also translated as “but”, but it is used after a negation, when you are correcting or replacing something:

Se ei ole heikkoa kahvia, vaan vahvaa.
It’s not weak coffee, but (rather) strong.

Key idea:

mutta = but / however (plain contrast, no prior negation required)
vaan = but rather / but instead (after ei or another negation)

In your sentence, there’s no negation, so mutta is the correct choice.

Can I change the order and say “Tämä kahvi on herkullinen mutta vahva”?

Yes, that is perfectly correct Finnish:

Tämä kahvi on vahva mutta herkullinen.
Tämä kahvi on herkullinen mutta vahva.

The difference is mostly in emphasis:

First version emphasizes that the coffee is strong, but despite that, it’s delicious.
Second version emphasizes that the coffee is delicious, but also strong.

It’s similar to English:

This coffee is strong but delicious vs. This coffee is delicious but strong.

Could I put the adjectives before the noun, like “tämä vahva mutta herkullinen kahvi”?

Yes. That is also correct, but the structure changes slightly:

Tämä kahvi on vahva mutta herkullinen.
– Predicate adjectives after the verb:
This coffee is strong but delicious.
Tämä vahva mutta herkullinen kahvi on kallista.
– Attributive adjectives before the noun:
This strong but delicious coffee is expensive.

In your original sentence, the focus is on making a comment about “this coffee” (what it is like). When you move the adjectives before kahvi, you are more labeling/classifying the coffee as “strong but delicious coffee” and then typically saying something further about it.

How would I say this in the plural: “These coffees are strong but delicious”?

You need:

plural demonstrative: nämä (these)
plural subject: kahvit
plural verb: ovat (3rd person plural of olla)
plural adjectives: vahvoja, herkullisia

So:

Nämä kahvit ovat vahvoja mutta herkullisia.
These coffees are strong but delicious.

Notice the changes:

Tämä kahvi on → Nämä kahvit ovat
vahva, herkullinen → vahvoja, herkullisia

How do I turn this into a yes/no question like “Is this coffee strong but delicious?”?

Finnish usually forms yes/no questions by adding -ko / -kö to a word (often the verb or the first element) and keeping word order mostly the same.

The most natural here is to attach it to on:

Onko tämä kahvi vahva mutta herkullinen?
Is this coffee strong but delicious?

Notes:

on → onko (because o takes -ko, not -kö)
The rest of the sentence stays in normal order.

Answers would be:

Kyllä on. – Yes, it is.
Ei ole. – No, it isn’t.

Any tips for pronouncing kahvi, vahva, and herkullinen correctly?

Some key points:

Stress is always on the first syllable in Finnish:
KAH-vi, VAH-va, HER-kul-li-nen.
h is clearly pronounced in kahvi and vahva; don’t drop it.
The v sound is between English v and w, made with the lips, not the teeth.
Double consonant in herkullinen (the ll) is held slightly longer:
HER-kul-li-nen, not HER-ku-li-nen.
Vowels are short here (no double letters), so keep them brief:
a as in father, e as in bet, i as in machine.

Putting it together:

Tämä kahvi on vahva mutta herkullinen.
→ TÄ-mä KAH-vi on VAH-va MUT-ta HER-kul-li-nen, with steady rhythm and clear consonants.