I'll offer my condolences to him about his father's death.

Literal

Father's death [matter-のことで] him [to-に] condolences say.

お悔やみを言う is the set expression for offering condolences. ~のことで marks the topic or reason — here, the father's death is the subject of the condolence. Polite condolence formulas like お悔やみ申し上げます are a key part of Japanese funeral etiquette.