Si tu n'aimes pas ce gâteau, je peux préparer autre chose.

French standard negation usually uses two parts: ne ... pas around the conjugated verb.

• tu aimes = you like
• tu n'aimes pas = you do not like / you don't like

The ne becomes n' before a vowel sound, which is why you see n'aimes.

In everyday spoken French, people often drop ne, so you may hear Tu aimes pas ce gâteau, but in careful written French, ne ... pas is the normal form.

The apostrophe shows elision: a vowel is dropped to make pronunciation smoother.

• ne aimes would sound awkward
• so French shortens it to n'aimes

This happens often in French before a vowel or silent h:

• je aime → j'aime
• ne aime pas → n'aime pas
• le ami → l'ami

Because gâteau is a masculine singular noun that starts with a consonant sound.

French uses:

• ce before a masculine singular noun starting with a consonant
  
  • ce gâteau
• cet before a masculine singular noun starting with a vowel or silent h
  
  • cet ami
  • cet homme

So gâteau takes ce, not cet.

Because the subject is tu.

The verb aimer in the present tense is:

• j'aime
• tu aimes
• il/elle/on aime
• nous aimons
• vous aimez
• ils/elles aiment

So with tu, the correct form is aimes.

Si means if.

In this sentence, si tu n'aimes pas ce gâteau sets up a real possible condition: if you don't like this cake.

A very common French pattern is:

• si + present tense, then a result in the present, future, or imperative

Here you have:

• Si tu n'aimes pas ce gâteau = if you don't like this cake
• je peux préparer autre chose = I can prepare something else

One important rule: French does not normally use the future tense right after si in this kind of sentence.

So French says:

• Si tu n'aimes pas..., je préparerai... not:
• Si tu n'aimeras pas...

In your sentence, the result clause uses peux because the speaker is expressing ability or willingness right now.

Because after pouvoir (can / to be able to), French uses the infinitive directly, with no extra word like de.

• je peux préparer = I can prepare
• tu peux venir = you can come
• nous pouvons partir = we can leave

English learners sometimes expect a preposition, but with pouvoir, you simply put the infinitive after it.

Autre chose means something else.

It is a very common expression:

• autre = other / another
• chose = thing

Together, autre chose works like something else, not literally another thing in the way English might analyze it.

Examples:

• Je veux autre chose. = I want something else.
• Tu as autre chose à manger ? = Do you have something else to eat?

Because autre chose is a fixed expression meaning something else.

French usually does not say une autre chose in this meaning. That sounds unnatural in standard French.

So:

• préparer autre chose = prepare something else

This is similar to other fixed expressions:

• quelque chose = something
• peu de chose = not much / little

Yes. That would be the polite or plural version.

Your original sentence uses tu, which is:

• singular
• informal

If you are speaking to one person politely, or to more than one person, use vous:

• Si vous n'aimez pas ce gâteau, je peux préparer autre chose.

The rest of the sentence stays almost the same; only the verb changes from aimes to aimez.

Yes. French can put the si clause first or second.

Both are natural:

• Si tu n'aimes pas ce gâteau, je peux préparer autre chose.
• Je peux préparer autre chose si tu n'aimes pas ce gâteau.

When the si clause comes first, a comma is commonly used. When it comes second, the comma is often omitted.

No. In French, gâteau is singular and is pronounced roughly ga-toh.

A few useful points:

• the â does not change the basic meaning here; it is part of the spelling
• the final eau sounds like oh
• the final x appears only in the plural gâteaux, and it is normally silent

So:

• gâteau = singular
• gâteaux = plural

But both end with the same final sound: oh.