a*3b\sqrt2=3ab\sqrt2
b)
x\sqrt5*y\sqrt3=xy\sqrt{5*3}=xy\sqrt{15}
c)
\frac{1}{3}a*\frac{a^2}{2}\sqrt6=\frac{1}{3}a*\frac{1}{2}a^2\sqrt6=\frac{1}{6}a^{1+2}*\sqrt6=\frac{1}{6}a^3\sqrt6
d)
-3x^5\sqrt3*x\sqrt6=-3x^5*x*\sqrt{3*6}=-3x^6\sqrt{18}=-3x^6\sqrt{9*2}=-3x^6*3\sqrt2=-9x^6\sqrt2
e)
9\sqrt2*x^3y^2*\frac{\sqrt{11}}{3}=3\sqrt2*x^3y^2*\sqrt{11}=3x^3y^2*\sqrt{2*11}=3x^3y^2\sqrt{22}
f)
3\sqrt2ab^2*(-a^3\sqrt3)=-3a^3*ab^2*\sqrt{2*3}=-3a^4 b^2\sqrt6