Reibun
、、。

When you sleep on your back, your tongue and uvula drop toward the back of the throat, making the upper airway more likely to be blocked.

Literal

Face-up [adverbial-に] sleep-[when-と], tongue [and-や] uvula [subject-が] throat-back [locative-に] drop-[because-ため], upper-airway [subject-が] become-easy-to-be-blocked.

A medical/popular-science style sentence. Note the classic conditional ~と, which here means 'whenever/when X happens, Y follows' — the natural-consequence conditional, typical of scientific and instructional writing. や is a non-exhaustive list particle ('A, B, among others'), distinct from exhaustive と. ノドチンコ is the colloquial word for the uvula; the formal/medical term is 口蓋垂 (こうがいすい). The ~やすい suffix on 塞がる converts the verb into 'easy to be blocked'.