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..
\(x^{2} * x^{2} = x^{4}\)
\(x^{2} *-2x=-2 x^{3}\)
\(x^{2} *2x=2 x^{3}\)
\(x^{2} *-2=-2 x^{2}\)
\(-2x*2x=-4 x^{2}\)
\(x^{2} *3=3 x^{2}\)
-22x=-4x
-2x3=-6x
-23=-6
Now..FINALLY...add it up..
Making the answer to your second equation...
\(x^{4} -2 x^{3} +2x ^{3} -6x ^{2} +3 x^{2} -10x-6\)
\(x^{4} -3x ^{2}-10x-6.\)