Después de cenar, prefiero un té de menta.

Because después normally needs the preposition de before a noun or an infinitive.

• después de cenar = after having dinner / after dinner
• después de la cena = after the dinner / after dinner

So de is required here.
A very common pattern is:

• después de + noun
• después de + infinitive

Examples:

• después de comer = after eating / after lunch
• después de trabajar = after working

After después de, Spanish uses the infinitive when the subject is general or understood.

So:

• después de cenar = after eating dinner / after dinner

You do not use a conjugated verb like ceno here.

Compare:

• Después de cenar, salgo. = After dinner, I go out.
• Después de trabajar, descansamos. = After working, we rest.

This is very natural in Spanish and often matches English structures like after eating, after working, etc.

Cenar specifically means to have dinner / to eat dinner / to dine.

It does not mean just to eat in general.
For to eat, Spanish uses comer.

So:

• comer = to eat
• cenar = to have dinner

That is why después de cenar is specifically after dinner, not just after eating in a broad sense.

Spanish often drops subject pronouns because the verb ending already shows who the subject is.

• prefiero = I prefer

The ending -o tells you it is yo.

So both are possible:

• Prefiero un té de menta.
• Yo prefiero un té de menta.

But the version without yo is more neutral and more common unless you want emphasis or contrast.

For example:

• Yo prefiero té, pero ella prefiere café.
  Here yo is used for contrast.

Because preferir is a stem-changing verb in the present tense.

The e in the stem changes to ie in most forms:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos/ellas prefieren

Notice that nosotros and vosotros do not change the stem.

This is a very common type of irregularity in Spanish, like:

• quiero from querer
• pienso from pensar

Because in this sentence, un té de menta means a mint tea or one mint tea as a drink.

Spanish often uses the indefinite article when ordering or referring to a drink:

• un café
• un té
• una cerveza

So:

• Prefiero un té de menta. = I prefer a mint tea.

You could also hear:

• Prefiero té de menta.

That sounds more like I prefer mint tea in a general sense, while un té de menta sounds like a specific serving/cup.

Té de menta is the normal way to say mint tea.

In Spanish, de is often used to describe the type or flavor of something:

• helado de chocolate = chocolate ice cream
• zumo de naranja = orange juice
• té de menta = mint tea

Té con menta is possible, but it usually sounds more like tea with mint added to it, not the standard name of the drink.

So if you mean the drink called mint tea, té de menta is the most natural choice.

Because té with an accent means tea, while te without an accent means you (object pronoun).

• té = tea
• te = you / to you

Examples:

• Quiero té. = I want tea.
• Te veo. = I see you.

The accent helps distinguish the two words.

Because Después de cenar is an introductory time phrase.

In Spanish, it is common to put a comma after an opening phrase like this, especially in writing:

• Después de cenar, prefiero un té de menta.

The comma helps separate the background information (after dinner) from the main statement (I prefer a mint tea).

In very short sentences, punctuation can sometimes vary, but this comma is completely standard and natural.

Yes. Tras cenar also means after dinner / after having dinner.

• Después de cenar = more common and very neutral
• Tras cenar = also correct, slightly more concise, sometimes a bit more formal or written in tone

For everyday speech, después de cenar is usually the safest and most common option.

Not if you want the same meaning.

• prefiero = I prefer
• me gusta = I like

These are different ideas.

So:

• Después de cenar, prefiero un té de menta. = After dinner, I prefer a mint tea.
• Después de cenar, me gusta tomar té de menta. = After dinner, I like to have mint tea.

If the English meaning is specifically about preference, prefiero is the right choice.

It can usually mean a general preference.

The present tense in Spanish often expresses habits, routines, and general likes:

• Después de cenar, prefiero un té de menta.

This sounds like:

• After dinner, I prefer mint tea.
• When it comes to after dinner, I’d rather have mint tea.

Depending on context, it could also refer to the current situation, but without more context it most naturally sounds like a general preference.

Yes, but it is slightly different.

• té de menta = mint tea
• infusión de menta = mint herbal infusion

In everyday use, people may say té de menta quite loosely, but technically té is tea and infusión is a herbal drink not made from tea leaves.

In Spain, you may also hear very natural drink names like:

• una manzanilla = camomile tea
• un poleo menta = pennyroyal mint infusion

So un té de menta is perfectly understandable and natural for learners, but una infusión de menta can sound a bit more precise.