It's not a stupid question. It is silly, but it is designed to make you think about how time zones work. The answer is no because time zones only mark local time on earth. When you cross a time zone you have to set your clock an hour ahead or back to be in synch with the local time.
If you are travelling from East to West at Mach 4, you will be travelling faster than the sun, so it will appear to get earlier as you go. You will travel from afternoom into morning into night.. You will have to set your clock back an hour each time you cross a time zone, which will happen every half hour or so. The sun crosses one time zone per hour, so you will see it set behind you in the East.
When you cross the IDL you will have to set your clock ahead 24 hours to counteract this effect. So the date will be 'tomorrow'. But as you continue around the world, you keep setting it back. When you get back to the IDL, you will have set it back 24 hrs, so it will be "today' again.
At Mach 4 you would go around the world in about 12 hrs. Suppose you cross the IDL at ten AM today, the 16th. When you cross the line it is suddenly ten AM the 17th. When you come around again it will be ten PM, but you will have set your watch back 24 hrs, so it will be 10 PM, the 16th, just before you cross the line, which will be the correct local time.
If you travel West to East everything happens in reverse. That is, you keep setting your watch ahead until you cross the IDL, then you set it back 24 hrs.
It's a pretty tricky question for sixth grade. A lot of adults don't really understand how time zones work.