The sentence La dame est venue avec ___ enfants means "The lady came with ___ children." The blank requires a possessive adjective that agrees with the plural noun enfants and refers to the lady (third-person singular feminine possessor).
The correct answer is ses. In French, ses is the possessive adjective for a singular possessor (he/she) with a plural noun. It means "his/her" before plural nouns, regardless of the possessor's gender.
The other options are incorrect:
son is the possessive adjective for a singular possessor with a masculine singular noun (or a feminine singular noun beginning with a vowel, e.g., son amie). Enfants is plural, so son does not agree
de is a preposition, not a possessive adjective
leur means "their" and would indicate multiple possessors. Since la dame is a single person, leur is incorrect
The French possessive adjectives for a singular possessor are: mon/ma/mes (my), ton/ta/tes (your), son/sa/ses (his/her). The form depends on the gender and number of the possessed noun, not the possessor.
