The stability of dihalides of Si, Ge, Sn and Pb increases steadily in the sequence

The elements Si, Ge, Sn and Pb belong to Group 14 (the carbon family).
For these elements the most common oxidation state is $$+4$$, but a lower oxidation state $$+2$$ is also observed.

Concept used - Inert-pair effect
• As we move down a p-block group, the valence-shell $$ns$$ electron pair is held more tightly (poor shielding of intervening d and f electrons).
• Hence it becomes increasingly difficult to promote these two $$ns$$ electrons into bonding orbitals.
• This reluctance is called the inert-pair effect and it stabilises the lower oxidation state $$+2$$ relative to $$+4$$ for heavier members of the group.

Applying the concept to Group 14:
• For Si the inert-pair effect is negligible, so the $$+4$$ state dominates and $$SiX_2$$ is extremely unstable.
• The effect appears gradually in Ge, becomes significant in Sn and is strongest in Pb.
• Therefore the order of stability of the $$+2$$ halides (dihalides) increases down the group.

Hence, $$SiX_2 \ll GeX_2 \ll SnX_2 \ll PbX_2$$.

So, the correct option is:
Option C which is: $$SiX_2 \ll GeX_2 \ll SnX_2 \ll PbX_2$$