Does it make sense to have a compression function that uses 64-bit of the message to create an output of 64-bit?
This hash function has a 64-bit output.  Therefore, it is not collision-resistant.  It is easy to find a collision in any hash function with a 64-bit output.  Since this appears to be a homework, I'm going to leave it to you to figure out why this is the case.

In general, please don't just post a homework question and expect us to solve it for you.  We're not here to solve your homework for you.  Instead, the expectation on this site is that you will show us in detail what you've tried and how far you've gotten, and explain where you got stuck.  Then we might be able to help get you unstuck.  But just posting the problem description from your homework, nothing more, and expecting us to hand you the solution on a platter is not what this site is for.  This isn't a "solve-your-homework-for-you" site.