Answer
$n \geq 8$
Work Step by Step
Consider the error bound for Simpson's Rule:
$|E_S| \leq \dfrac{M(b-a)^5}{180n^4}$
The maximum value of $|f^{4}(x)|$ on $[1,2]$ is equal to:
$M=3$
Now, $|E_S| \leq \dfrac{3 \times(2-1)^5}{180n^4}=\dfrac{1}{60n^4}$
We will choose $n$ such that $\dfrac{1}{60n^4} \leq 10^{-5}$
Thus, $n \geq 6.4 \approx 7$
As per Simpson's Rule, we consider only the even value of $n$, so $n \geq 8$
