。
You can watch TV after dinner.
Literal
Dinner-of after TV [object-を] watch-[permission-てもいい]-[polite-ですよ].
~てもいい is the permission form — 'it's okay even if you do X,' meaning 'you may X.' Literally 'even-if you watch TV, it's good.' Common as a generous permission from a parent or host; the よ at the end makes it inviting rather than a neutral statement.