Ok, this is off of the tab for the song Plateau, played in Nirvana's Unplugged album.

I was wondering how do i play this?

more specifically this, how do I do that? do i finger pick both of them or do i hit them separately?

uh, obviously >_> I mean which fashion do i pick them? finger picking or do i pick them alternatively?
Probably fingerpick em, or pick the low E with your pick and the high e with your finger.
with this song pick both of them and it helps if you use the major G chord finger grouping for this phrase