First solve the equation $\alpha^{3} - 6\alpha ^{2} +12\alpha -8=0$
So, here $\alpha=2,2,2$
Now, for particular solutions,
For $c)$ root $2$ has multiplicity $m=3$
So,
$a_{n}^{(p)} = n^{3}(P_{1}n + P_{0})2^{n}$
Put it in recurrence and find $P_1$ and $P_0$
For $e)$
$a_{n}^{(p)} = n^{3}(P_2n^2+P_{1}n + P_{0})2^{n}$
Put it in recurrence and find $P_2,P_1$ and $P_0$
For $f)$
$a_{n}^{(p)} = (P_3n^3+P_2n^2+P_{1}n + P_{0})(-2)^{n}$
Put it in recurrence and find $P_3,P_2,P_1$ and $P_0$