Make sure the patient receives proper care.

Literal

Sick-person [subject-が] proper care [object-を] can-receive [so-that-ようにしなさい].

適切な看護を受けられるようにしなさい layers multiple patterns: 受けられる (potential form), ようにする ('make sure that'), なさい (polite imperative). The construction means 'make arrangements so that the patient can receive care.'