。
Explain the reasons properly — state them as thus and such.
Literal
Reason [topic-は] thus-and-such [copula-であると] properly explain [imperative-なさい].
こうこう is a reduplication meaning 'such-and-such, thus-and-so' — a placeholder for specific content. であると is the formal copula + quotative particle, framing the reasons as reported content. ちゃんと means 'properly.' ~なさい is the mild imperative (from なさる), softer than しろ but still commanding — typically parent-to-child or teacher-to-student.