You're on vacation, but you're not really sure what you want to do. You're usually so busy, so you don't remember how to relax and enjoy vacation time. You say to your husband:
With all this down time, I don't know what to do with myself!
This is hard to explain! But when you want to tell the context or the reason for a comment, you explain it with the word "with". For example:
With all the rain we've been having, I bet we'll get some great strawberries this year.
With the time you put into studying, you should do really well on the TOEIC.
"Down time" is time when you're not doing work or other necessary activities. Some things that you can do in your "down time" are going out with friends, watching TV, relaxing on the beach, or surfing the Internet.
This is a common English idiom which just means that you don't know what to do. But "I don't know what to do with myself" sounds more colorful and friendly.
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