how long does it take for apple to fix ipod touch,

We have no way of knowing. This is a user to user forum, not Apple.

Might be help here > Apple - Support - Service Answer Center

Hi,

they took 2 days to fix mine (from the Time UPS came to pick it up to when i got it back in the morning 2 days later), thats about the time it takes.

of course if you sent it you should have a UPS tracking number that you can input into the web site and they give you the tracking. Then in the apple site you can find the repair status.

Hope it helps

Cheers 😊

In most cases they do not "fix" your original phone, but rather send you a refurbished equivilent. Therefore, it only takes processing and transport time (and, if its a warranty repair, I assume they also determine whether the problem was caused by the user--such as a broken screen--or is a product defect).