Using the definition of GD and the requirements in the problem statement we are looking for $\eta$ such that:
$$
x_*=x_t-\eta \nabla f\left(x_t\right) \Longleftrightarrow 0=2-\eta \nabla f(2) \Longleftrightarrow \eta \cdot(2 \cdot 2)=2 \Longleftrightarrow \eta=\frac{1}{2}
$$
