Verified answer

in your example:

(-4m - 4n- 8) - (-6n - 2),

let's get rid of the parentheses, so we have:

-4m - 4n - 8 + 6n + 2

collect all the m-terms:

well, we only have 1, so there's nothing to do.

collect all the n-terms:

-4m - 4n - 8 + 6n + 2 = -4m + (-4n + 6n) - 8 + 2

= -4m + 2n - 8 + 2

now that we're done with the m-terms and n-terms, collect all the constant terms (plain old ordinary numbers):

-4m + 2n - 8 + 2 = -4m + 2n + (-8 + 2)

= -4m + 2n - 6

that's it.

now, if you had exponents, you would want to put all the m^3 together, all the m^2 together,

and then the m-terms together, and so on with n^3, n^2, then n-terms.

so the basic way to organize the "like terms" is:

first variable: highest power to lowest power

second variable: same

.....

.....

constants

if you have "mixed monomials" like x^3y^2 or xy^3, every combination of variable/powers can only be added (or subtracted) to the exact same combination, x^2y and xy do not mix, for example.