たらどうWhy don't you...?, What if you did...?

ませんか is a polite way to extend an invitation, similar to 'Won't you…?' or 'Wouldn't you like to...?' in English. In contrast, たらどう has a stronger tone and is used to suggest or advise a course of action. For example, 何か食べませんか？ is a polite offer (e.g. to a guest), while 何か食べたらどう？ implies the speaker thinks the listener should eat something.

たらどう is a gentle, open-ended suggestion, e.g. 休んだらどう？('Why don't you take a break?'). たらいい・といい can also suggest, but sounds more like advice, e.g. 休んだらいいよ ('You should take a break.'). It can also express hope, like 雨が止むといいね = 'I hope the rain stops.'.

たら expresses a condition or hypothetical, and when combined with どう, forms a casual suggestion. For example, 散歩に行ったらどう？ means 'How about going for a walk?'. Similar to the English phrase 'Why don't you (A)?' or 'How about (A)?', it isis common in informal conversation.

The imperative or command form (命令形) is used for blunt orders, e.g. 止まれ ('Stop!'), which can be harsh. In contrast, たらどう is a soft suggestion, similar to 'Why don't you (A)?' in English, e.g. 行ってみたらどう？ ('Why don't you try going?'). It gives the listener more freedom and therefore sounds more gentle.

Both たらどう and たほうがいい can be used to give advice or suggestions. The key difference is that たほうがいい has a strong nuance that the speaker is advising the listener on what to do or what would be the best course of action ('You should...'), while たらどう is more gentle, as if suggesting a potential option but not strongly insisting on it ('How about if you...?')