Learn Italian: Sto intrattenendoli in giardino, ma sono esausto. - I am entertaining them in the garden, but I am exhausted.

When using the progressive tense (stare + gerund), you have two choices for object pronouns like li (them). You can attach them to the end of the gerund to form a single word (intrattenendoli), or you can place them before the conjugated verb (Li sto intrattenendo). Both are perfectly correct.

The verb is intrattenere. How is its gerund formed?

Intrattenere (to entertain) is built from the verb tenere (to hold). To form the gerund, you follow the regular -ere pattern for tenere, which gives you tenendo, and simply add the prefix to get intrattenendo.

Why do we use in giardino without an article like nel?

In Italian, many common areas around the home take the simple preposition in without a definite article. Just as you would say in cucina (in the kitchen) or in bagno (in the bathroom), you say in giardino for the garden.

Would the ending of esausto change if a woman were speaking?

Yes. Esausto (exhausted) is an adjective that must agree in gender and number with the subject. If the person speaking is a woman, she would say sono esausta.