Remember the word FOIL. F for FIRSTS, O for OUTERS, I for INNERS, 
and L for LASTS.

-------------------------------------------

The FIRSTS are the 7y² and the y²

(7y²+x)(y²-2x)

That's because the 7y² comes FIRST in the (7y²+x)
and the y² comes FIRST in the (y²-2x)

So we multiply them together

7y²·y² = 7y4

---------------------------------------------

The OUTERS are the 7y² and the -2x

(7y²+x)(y²-2x)

That's because the 7y² and the -2x are on the OUTSIDE
(That is they are the farthest OUT from each other)

So we multiply them together

7y²·-2x = -14xy²

------------------------------------------------

The INNERS are the +x and the y²

(7z²+x)(y²-2x)

That's because the +x and the y² are on the INSIDE
(That is they are in the middle)

So we multiply them together

+x·y² = +xy²

----------------------------------------

The LASTS are the +x and the -2x

(7y²+x)(y²-2x)

That's because the +x comes LAST in the (7y²+x)
and the -2x comes LAST in the (y²-2x)

So we multiply them together

+x·-2x = -2x²

------------------------------------------

Write down the four terms from above for FIRSTS, OUTERS, INNERS, and LASTS:

7y4-14xy²+xy²-2x²

The two middle terms are like terms, so they will combine as -13xy²

Answer: 7y4-13xy²-2x² 

Edwin