Expand the second set of brackets and group like terms.
(8x^(2)+18xy+9x^(2))-(x^(2)+3xy+2y^(2))
Since 8x^(2) and 9x^(2) are like terms, add 9x^(2) to 8x^(2) to get 17x^(2).
(17x^(2)+18xy)-(x^(2)+3xy+2y^(2))
Multiply -1 by each term inside the parentheses.
17x^(2)+18xy-x^(2)-3xy-2y^(2)
Since 17x^(2) and -x^(2) are like terms, add -x^(2) to 17x^(2) to get 16x^(2).
16x^(2)+18xy-3xy-2y^(2)
Since 18xy and -3xy are like terms, add -3xy to 18xy to get 15xy.
16x^(2)+15xy-2y^(2)
Hope that helps