I'm not even sure you *could* upgrade to Peppermint 6 .. if we put you on Peppermint 3 it was for one of two reasons
a) system specs were too low for Peppermint 6
or
b) your CPU doesn't support PAE, which is required for Peppermint 4 onwards.
Easy way to find out if it was (b), what's the output from:
cat /proc/cpuinfo | grep flags