Learn French: Ils paient toutes les dépenses avec ce chèque. - They are paying all the expenses with this check.

The verb is payer. For verbs ending in -yer, the y changes to an i whenever the ending is silent (like with je, tu, il/elle, and ils/elles). Because the subject here is ils, we use the i spelling: paient. Note that for payer specifically, both spellings (paient and payent) are technically correct, but the i spelling is much more common.

Do I pronounce the '-ent' at the end of paient?

No! In French, the -ent ending on a verb for ils or elles is always completely silent. You just pronounce the stem, so paient sounds exactly like the French word paie, with no 'n' or 't' sound at all.

Why is it toutes les dépenses instead of tous les dépenses?

The word for 'all' (tout) must agree in gender and number with the noun it describes. The noun dépense (expense) is feminine, and here it is plural, so you need the feminine plural form: toutes.

Why is it ce chèque and not cette chèque?