Log6 ^x+log6^y=3

does log6 ^x mean log(6^x) or log6(x) ?

try log_6(xy) = 3
xy = 6^3 = 216
can't do much with that.

Maybe you meant
log 6^x + log 6^y = 3
log 6^(x+y) = 3
6^(x+y) = 10^3 = 1000
still not much to be done with that.