C(OH)₄ is unstable because a carbon atom cannot hold more than one –OH but Si(OH)₄ is a stable compound because

Silicon atom due to bigger size cannot from strong $\mathrm{p\pi }-\mathrm{p\pi }$ bonds with oxygen by eliminating water.

Carbon can form strong $\mathrm{p\pi }-\mathrm{p\pi }$ bond with oxygen by eliminating water

Silicon being more electronegative than carbon can hold four OH groups.

Silicon can form strong $\mathrm{d\pi }-\mathrm{p\pi }$ bond with lone pairs on oxygen .