Valency is the number of electrons in the outermost shell, or the maximum number of electron that is required to attain its nearest noble gas configuration.
Since Carbon has an electronic configuration 1s2 2s2 2p2 is short of four electron to acquire its nearest noble gas configuration i.e, Neon, having an electronic configuration 1s2 2s2 2p6.
Do note , for an element like Carbon it requires 4 electron to complete its octate it needs to fill up p orbital which can accommodate upto 6 electron.
