Shear Modulus & Poisson's Ratio question from JEE Main 2025 (4 Apr, Shift 1)

Two slabs with square cross section of different materials $(1, 2)$ with equal sides $(l)$ and thickness $d_1$ and $d_2$ such that $d_2 = 2d_1$ and $l > d_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_2 = 2\theta_1$. If the shear moduli of material 1 is $4 \times 10^{9}\text{ N/m}^2$, then shear moduli of material 2 is $x \times 10^{9}\text{ N/m}^2$, where value of $x$ is ________.