Looking along the common axis from $C_1$’s side: $C_1$ is anti-clockwise, so its field through $C_2$ points away from $C_1$ (let’s call this $+\hat{i}$). $C_3$ is clockwise as viewed from its own side, so from $C_2$’s perspective $C_3$’s field also points in the $+\hat{i}$ direction through $C_2$. So both coils contribute flux in the same direction through $C_2$.

Net flux through $C_2$: $\Phi =(B_{C_1}+B_{C_3})\cdot A$ in $+\hat{i}$.

For an induced current in $C_2$ to flow clockwise (as viewed from $C_1$’s side), the induced field inside $C_2$ must point in $-\hat{i}$ — meaning $C_2$ is opposing an increase in $+\hat{i}$ flux. So the net flux through $C_2$ must be increasing.

Bringing $C_1$ closer increases $B_{C_1}$ through $C_2$; moving $C_3$ away decreases $B_{C_3}$ through $C_2$. For net flux to still increase, the gain from $C_1$ approaching must outweigh the loss from $C_3$ receding — this is what option (2) describes (and it matches the expected behaviour symmetric with the asymmetric current directions).

Among the four options, (2) is the correct case.