Simple...
[tex](3x y^{3} )(2 x^{3}y) [/tex]
3*2=6
[tex]x* x^{3}= x^{4} [/tex] (Exponents "multiplied" are added)
[tex] y^{3} *y= y^{4} [/tex]
Making it...
[tex]6 x^{4}y ^{4} [/tex]
Thus, the answer to your first question.
The Second One....
[tex] (x^{2} -2x-2)*( x^{2} +2x+3)[/tex]
It looks hard, but it's not...break it down..
[tex] x^{2} * x^{2} = x^{4} [/tex]
[tex] x^{2} *-2x=-2 x^{3} [/tex]
[tex] x^{2} *2x=2 x^{3} [/tex]
[tex] x^{2} *-2=-2 x^{2} [/tex]
[tex]-2x*2x=-4 x^{2} [/tex]
[tex] x^{2} *3=3 x^{2} [/tex]
-2*2x=-4x
-2x*3=-6x
-2*3=-6
Now..FINALLY...add it up..
Making the answer to your second equation...
[tex] x^{4} -2 x^{3} +2x ^{3} -6x ^{2} +3 x^{2} -10x-6[/tex]
[tex] x^{4} -3x ^{2}-10x-6. [/tex]
