Puc ajudar la mare, però el gat no pot sortir.

Puc means I can or I am able to. It comes from the verb poder, which means to be able to / can.

So:

• puc = I can
• pot = he/she/it can

Poder is an irregular verb, so its forms do not all look very similar.

Catalan often leaves out subject pronouns when they are clear from the verb form.

So:

• Puc ajudar... already tells you the subject is I
• adding jo is possible, but not necessary

This is very common in Catalan. The verb ending often gives enough information by itself.

Because the subject changes.

• In Puc ajudar la mare, the subject is I, so the verb is puc
• In el gat no pot sortir, the subject is the cat, which is third-person singular, so the verb is pot

The verb poder has to agree with its subject.

After poder, the next verb normally stays in the infinitive.

So:

• puc ajudar = I can help
• pot sortir = can go out / can leave

This works much like English:

• I can help
• the cat can go out

You do not conjugate the second verb here.

In Catalan, no usually goes before the conjugated verb.

So:

• no pot sortir = cannot go out

The negation is attached to pot, the finite verb. This is the normal way to make a sentence negative in Catalan.

They are the definite articles the:

• la mare = the mother
• el gat = the cat

Catalan uses definite articles very regularly. With family words like mare, the article is also very natural, and depending on context it can sometimes sound more natural in Catalan than a literal English the mother would.

Because la mare is the direct object of ajudar.

In this sentence:

• puc = main verb
• ajudar = infinitive
• la mare = the person being helped

Standard Catalan normally does not need an extra preposition here. So ajudar la mare is the normal pattern.

Però means but.

The accent on ò helps show:

• where the stress falls
• that the vowel is an open o sound

So the word is pronounced with stress on the second syllable: pe-RÒ.

It can mean either, depending on context.

Common meanings include:

• to go out
• to leave
• to come out

In this sentence, with the cat, go out is probably the most natural translation:

• el gat no pot sortir = the cat can't go out

Yes. A comma before però is very normal when it joins two clauses.

Here the sentence has two parts:

• Puc ajudar la mare
• però el gat no pot sortir

So the comma helps separate the contrast, just like in English before but.