This can be found out using generating function
$\text{A - 1, C - 1, I - 2, S - 3, T - 3}$
$\underbrace{A}\ \ + \ \underbrace{C} \ \ \ + \ \underbrace{I}\ \ \ \ + \ \underbrace{S}\ \ \ \ + \ \underbrace{T}\ = 4$
$ \leq 1 \ \ \ \ \ \ \leq 1 \ \ \ \ \ \ \ \ \ \ \leq2 \ \ \ \ \ \ \ \ \ \ \leq 3 \ \ \ \ \ \ \ \ \ \ \leq3$
Now we need to find those coefficients whose power is 4
$\Rightarrow (1+x)(1+x)(1+x + x^2)(1+x+ x^2+x^3)(1+x+ x^2+x^3) $
$\Rightarrow (1+x)^2 \dfrac{(1-x^3)}{(1-x)} \dfrac{(1-x^4)}{(1-x)} \dfrac{(1-x^4)}{(1-x)}$
solving this equation we will get $34$ as answer