My mother told him to take care of his younger brother.

Literal

Mother [topic-は] him [to-に] younger-brother [possessive-の] care [object-を] do-[soft-command-なさい] [quotative-と] said

世話をしなさい = 'take care of (him)' — ~なさい as a direct command within quoted speech. と言った marks the speech act.