Hey there!
When multiplying two polynomials together, you will take the terms of the first polynomial and multiply them by each term of the second polynomial. The easiest way to do this is multiply every term in the second polynomial by the first term of the first polynomial, then repeat this with the second term of the first polynomial, like so:
(6x – y)(2x – y + 2)
6x × 2x = 12x²
6x × –1y = –6xy
6x × 2 = 12x
–1y × 2x = –2xy
–1y × –1y = 1y
–1y × 2 = –2y
Recall that if you multiply x by itself once that it become x². Also, if you multiply x times y, the term becomes xy. If there isn't a number before an unknown term, there will be an implied "1" before it. If a term like this is negative, it will have an implied "–1". Always put x before y when arranging your polynomials and terms.
The last thing to do is combine your like terms. You can only combine terms that have the exact same exponent and unknown term letters. You can rearrange your terms however you like when combining.
12x² – 6xy + 12x – 2xy + 1y – 2y
12x² – 6xy – 2xy + 12x + 1y – 2y
12x² – 4xy + 13x – 2y
Your final product will be (12x² – 4xy + 13x – 2y).
Hope this helped you out! :-)