Learn Italian: Gli uomini hanno comprato due bei ritratti e tre begli specchi. - The men bought two beautiful portraits and three beautiful mirrors.

The adjective bello changes its plural form based on the letter the next word starts with, following the exact same rules as the plural words for 'the' (i and gli). Because we say i ritratti, we use bei. But because specchi starts with an 's' plus a consonant, it takes gli, so the adjective becomes begli.

What happens if I put the adjective after the nouns instead of before them?

The special forms like bei and begli are only used when the adjective comes right before the noun. If you put it after the noun, it acts like a normal adjective and just uses the standard plural ending for masculine nouns, which is belli. You would say ritratti belli and specchi belli.

Why is the article Gli used for uomini here?

Uomini is the irregular plural of uomo (man). Because it starts with a vowel, the plural word for 'the' has to be gli. If it started with a normal consonant, you would use i.

Why is the verb hanno comprato used here to mean 'bought'?

This is the past tense, called the passato prossimo. Just like in English when we say 'they have bought', Italian builds this tense with a helper verb (hanno, meaning 'they have') and the past participle (comprato, meaning 'bought'). You need both words to complete the past tense verb.