The garage is 186' from the service at the house. I wanted to make sure the voltage drop would not cause a problem.

If you can find it, you can use #2/0 aluminum 4 wire SER cable. If not then #4/0 is readily available, a bit over sized, but will work fine.

With either size, you will have problems with the lugs at the new panel and the breaker at the Main Panel.

You will need to splice short pieces of #2 Al XHHW wire onto the larger wire at both ends.