3n+2m-6=4m+n there is no general solution here...there are actually infinite soutions !!!
add 6 to both sides
3n + 2m = 4m + n + 6
subtract 4m, n from both sides
2n - 2m = 6
factor the left side
2(n - m) = 6
divide both sides by 2
n - m = 3 → n = m + 3
and that's all we can do