#### Answer

$-5x^{2}+12xy+4y^{2}$

#### Work Step by Step

We are given $(3x^{2}+6xy+3y^{2})-(8x^{2}-6xy-y^{2})$. To subtract two polynomials, we can add the opposite of the second polynomial to the first polynomial.
$(3x^{2}+6xy+3y^{2})+(-8x^{2}+6xy+y^{2})$
Next, we can combine like terms.
$(3x^{2}-8x^{2})+(6xy+6xy)+(3y^{2}+y^{2})=-5x^{2}+12xy+4y^{2}$