Let $R=\Bbb Z[T], X = Spec\ R, \mathfrak m := (T − 2, 3)$ where $\mathfrak m$ is a maximal ideal of $R$.
Compute $\mathscr O_X (X − \{x\})$ where $x\in X$ corresponds to $\mathfrak m$.
We have $X − \{x\}=D(T-2) \cup D(3)$ where $D(f)$ are the affine open of X corresponding to $f\in R$.
Hence $\mathscr O_X (X − \{x\})=\mathscr O_X (D(T-2)) \cup \mathscr O_X (D(3)) $ which is equal to the set of elements of $\Bbb Q(T)$ of the form $\frac{P}{(T-2)^i}, i\in \Bbb N, P\in \Bbb Z[T]$ or of the form $\frac{P}{(3)^i}, i\in \Bbb N, P\in \Bbb Z[T]$.
But looking at the hint, $\mathscr O_X (X − \{x\})=\Bbb Z[T]$.
I don't understand, thank you for your help.