The other me is the Dr. Emmett Brown from 1955, the younger me that helps the other you get back to 1985.
10 seconds sound clip from the Back to the Future Part II movie soundboard.
You can hear this line at 01:03:30.776 in the Blu-ray version of the movie.
Quote context
[...]
- You don't have to remind me of that, Doc.
- Here's some binoculars and a walkie-talkie so we can keep in contact.
- I'll stay here and try to repair the short in the time circuit.
- Yes. There are now two of me here, and there are two of you here.
- Remember the lightning bolt at the clock tower?
- Yeah.
- I have to be prepared for all monetary possibilities.
- Get yourself some '50s clothes.
[...]