〜たらどうですか

た-form + らどうですか makes a suggestion: 少し休んだらどうですか, "why don't you rest a bit?" Literally "how would it be if you rested?"

Casually it's たらどう?: 先生に聞いたらどう? The polite version swaps in いかが: タクシーで行ったらいかがですか.

It's gentler than ほうがいい ("you should"), which sounds more like a recommendation from experience. But it's still advice, so with superiors it can come across as telling them what to do; a question about what they'd like is safer.

A reply that accepts the idea is often そうですね or そうします ("I'll do that").