She had the boys paint the house.

Literal

She [topic-は] boys [to-に] house [on-に] paint [object-を] made-paint.

塗らせた is the causative past of 塗る (ぬる, 'to paint, to apply'). The causative ~せる makes the boys do the painting. The に marks the boys as the people being made to act. ペンキ is a loanword from Dutch (pek/verf), reflecting the Netherlands' historical role as Japan's main Western trading partner during the Edo period.