Question 394836
e. 
{{{Var (X) = E(X^2)  - (E(X))^2}}}
<==> {{{4 = E(X^2) - 8^2}}}
==> {{{E(X^2) = 68}}}
==> {{{E(Y) = E(3X^2 + 2) = 3E(X^2) + 2 = 3*68 + 2 = 206 }}}


Now 

 {{{Var (Y) = Var(3X^2  +2) = 9Var (X^2)}}}
={{{9(E(X^4) - (E(X^2))^2)}}}
={{{9E(X^4) - 9*68^2 = 9E(X^4) - 41616}}}.

Hence {{{Var(3X^2  +2) = 9E(X^4) - 41616}}}.
{{{E(X^4)}}} is the 4th moment about the origin, and can't be evaluated without knowledge of the density function.