Кабачок мягче, чем баклажан, но мне нравятся оба.

Мягче is the normal comparative form of мягкий (soft).

In Russian, many adjectives form a short comparative in one word:

• мягкий → мягче = softer
• быстрый → быстрее = faster
• дорогой → дороже = more expensive

So:

• Кабачок мягче, чем баклажан = Zucchini is softer than eggplant

You can sometimes use более + adjective for more ..., but with common adjectives like мягкий, the one-word comparative мягче is much more natural.

This is a common sound change in Russian comparatives.

The adjective мягкий ends in -кий, and in the comparative it changes to -че:

• мягкий → мягче

This is just something you learn as part of the adjective’s comparative form. It is not fully predictable from English, so it is best memorized.

A few similar examples:

• лёгкий → легче = easier / lighter
• громкий → громче = louder
• тонкий → тоньше = thinner

So мягче is simply the standard comparative form meaning softer.

Чем means than in comparisons.

So:

• мягче, чем баклажан = softer than eggplant

This is the standard way to compare two things in Russian:

• Он выше, чем я. = He is taller than I am / me.
• Сегодня теплее, чем вчера. = Today is warmer than yesterday.

So in this sentence, чем introduces the second part of the comparison.

After чем, Russian usually keeps the noun in the form you would expect as a normal noun phrase, often nominative here:

• Кабачок мягче, чем баклажан

That is the most straightforward pattern for learners:
comparative + чем + noun/pronoun

There is also another comparison pattern in Russian where the second noun can appear in the genitive without чем:

• Кабачок мягче баклажана

Both mean the same thing: Zucchini is softer than eggplant.

Very roughly:

• мягче, чем баклажан = comparison with than
• мягче баклажана = a more compact comparison

For learners, the чем + noun pattern is often easier to understand and use.

Because нравиться works differently from English to like.

Russian uses a structure closer to:

• Something is pleasing to me

So:

• мне = to me
• нравятся = are pleasing
• оба = both

Literally, the phrase is something like:

• Both are pleasing to me

That is why Russian says:

• мне нравится... / мне нравятся...

not:

• я нравлюсь...

In fact, я нравлюсь means I am pleasing / likable, not I like.

Examples:

• Мне нравится фильм. = I like the film.
• Мне нравятся фильмы. = I like films.

Because the subject is оба = both, which refers to two things, so the verb must be plural.

Compare:

• Мне нравится кабачок. = I like zucchini.
  singular thing → нравится

• Мне нравятся кабачок и баклажан. = I like zucchini and eggplant.
  two things → нравятся

• Мне нравятся оба. = I like both.
  both = plural → нравятся

So the verb agrees with what is pleasing, not with мне.

Мне is the dative case of я.

Russian uses the dative with нравиться because the person is treated as the receiver of the feeling:

• мне = to me
• тебе = to you
• ему / ей = to him / her

Examples:

• Мне нравится кофе. = I like coffee.
• Тебе нравится эта книга? = Do you like this book?
• Ей нравятся цветы. = She likes flowers.

So in мне нравятся оба, мне is exactly the form Russian requires.

Оба means both.

Russian has two forms:

• оба for masculine and neuter
• обе for feminine

In this sentence, the two nouns are:

• кабачок — masculine
• баклажан — masculine

So the correct form is:

• оба

Examples:

• оба брата = both brothers
• оба окна = both windows
• обе сестры = both sisters

Since both vegetables here are grammatically masculine, оба is correct.

Russian has no articles. There is no direct equivalent of English a/an or the.

So:

• Кабачок can mean a zucchini, the zucchini, or zucchini
• баклажан can mean an eggplant, the eggplant, or eggplant

The exact meaning depends on context.

That is completely normal in Russian. Learners usually need to get used to understanding definiteness from the situation rather than from an article.

Yes. Russian word order is more flexible than English, although not completely free.

The neutral order here is:

• Кабачок мягче, чем баклажан, но мне нравятся оба.

This sounds natural and clear:

1. first the comparison
2. then the contrast with но (but)
3. then I like both

You could change the order for emphasis, for example:

• Но оба мне нравятся. = But I like both.
• Мне оба нравятся. = I like both.

These are all grammatical, but they shift emphasis slightly. The original sentence is a very natural neutral version.

Because но means but, and in Russian it normally joins two clauses with a comma before it.

So:

• Кабачок мягче, чем баклажан, но мне нравятся оба.

This is the same basic idea as in English:

• Zucchini is softer than eggplant, but I like both.

Russian punctuation is quite regular here: when но connects two parts like this, you usually put a comma before it.