。
Young children should be exposed to fine music.
Literal
Young child [object-を] outstanding music [to-に] touch-[causative-させる] should-[べき].
触れさせる is the causative of 触れる ('touch / come into contact with') — 'make [someone] touch.' 音楽に触れる ('come into contact with music') is a metaphorical expression for exposure. べき is the 'should' modal. A pedagogical recommendation.