If I ask a girl out and she says "I'll let you know" should I wait and ask her again?

My brother and an aunt of mine told me I should wait for 2 weeks and then tell her something like "hey, you forgot to tell me when we can hang out".

They recommended me to do that because she could've forgotten due to her schedule.

I know you guys will say "she is turning down" or something like that because, hey, we always have to think the worse and we can never be positive, right? Hahahahaha but asking you guys is a risk I'm willing to take... so, what do you think?

If I ask a girl out and she says "I'll let you know" should I wait and ask her again?
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