What's wrong with my calculation of Variance?

Question

Given $X_i$ ~ $Uni(0, 0.5)$ and $N$ ~ $Poisson(24)$ where $Y=\sum_{i=1}^{n}X_i$ I want to cauculate $Var(Y)$.

Here's my approach:

$Var(Y)=E(Y^2)-E(Y)^2$ Where it's given (to make calculations shorter) that $E(Y)=6$ so we get:

$Var(Y)=E(Y^2)-36$

We know that:

$E(Y^2)=E(E(Y^2)|N)$

$E(E(Y^2)|N=n) = n^2/12 + n/6$

So we get:

$E(Y^2)=E(E(Y^2)|N) = E(N^2/12 + N/6) = 600/12 + 4$

So:

$Var(Y)=50+4-36=18$

But the final answer is 2, what did I do wrong here?