Verified Answer :

Simple...

\((3x y^{3} )(2 x^{3}y)\)

32=6

\(x* x^{3}= x^{4}\)  (Exponents "multiplied" are added)

\(y^{3} *y= y^{4}\)

Making it...

\(6 x^{4}y ^{4}\)

Thus, the answer to your first question.

The Second One....

\((x^{2} -2x-2)*( x^{2} +2x+3)\)

It looks hard, but it's not...break it down..

\(x^{2} * x^{2} = x^{4}\)

\(x^{2} *-2x=-2 x^{3}\)

\(x^{2} *2x=2 x^{3}\)

\(x^{2} *-2=-2 x^{2}\)

\(-2x*2x=-4 x^{2}\)

\(x^{2} *3=3 x^{2}\)

-2
2x=-4x

-2x3=-6x

-2
3=-6

Now..FINALLY...add it up..

Making the answer to your second equation...

\(x^{4} -2 x^{3} +2x ^{3} -6x ^{2} +3 x^{2} -10x-6\)

\(x^{4} -3x ^{2}-10x-6.\)