Learn Italian: Non ce la faccio ad ascoltare un'altra offerta. - I can't manage to listen to another offer.

The infinitive is farcela, which means "to manage," "to succeed," or "to cope." It is made of the verb fare (to do/make) plus two fixed little words: ce and la. When conjugated, fare changes to match the subject (here, faccio for "I"), and the ce and la separate and move in front of the verb.

Does the la in ce la faccio refer to the feminine word offerta?

No! In the verb farcela, the la is a fixed part of the idiom. It never changes to match a noun in the sentence. It is just like saying "I can't manage it" in English, where "it" is just a general concept rather than a specific object.

Why is there an ad before ascoltare instead of just a?

The verb farcela requires the preposition a when it is followed by another verb in the infinitive (like ascoltare). Because ascoltare starts with the vowel "a", the preposition a changes to ad to make the two words sound smoother when spoken together.

Why isn't there an Italian word for "to" after ascoltare?