(6a-5y)(7a+3y)

Distribute the red parenthetical expression 
taken as a whole, into the blue parenthetical
expression:

(6a-5y)(7a) + (6a-5y)(3y)

Reverse the order of multiplication in each 
of the two terms:

7a(6a-5y) + 3y(6a-5y)

Now distribute the blue factors into the red 
parenthetical expressions, getting these purple
terms:

42a²-35ay + 18ay-15y²

42a² - 35ay + 18ay - 15y²

Combine the middle two like terms as -17ay

42a² - 17ay - 15y²  

Edwin