「めがねなくても大丈夫なの？」「あ、これ伊達めがねだから、頭よくなるかなと思って」

「？」「、、」

'Are you okay without your glasses?' 'Oh, these are just fashion glasses — I thought maybe they'd make me smarter.'

Literal

'Glasses without [even-ても] okay [question-なの]?' 'Ah, this fashion-glasses [reason-だから], head good become [wonder-かなと] think'

伊達めがね 'fashion glasses' — glasses without prescription lenses worn as an accessory. 伊達 (date) here means 'for show, for style' (from the Date clan, known for flamboyance). 頭よくなるかな 'I wonder if I'll get smarter' — a humorous, self-deprecating reason. The punchline is charmingly naive.