？
How about putting in contacts?
Literal
Contacts [object-を] put-in [quotative-という] [nominalizer-の] [topic-は] how-about [copula-でしょう]?
Polite suggestion pattern: [proposed action] + というのはいかがでしょう ('what about the idea of ~?'). というのは nominalizes the preceding clause into a discussable topic, and いかが is the polite form of どう. でしょう softens it into a tentative question. コンタクトを入れる is the idiomatic collocation for 'to put in contact lenses' — not 付ける or かける.