Question

why carbon cannot make it 4 bonding though it has 4 valency??????

Answer 1

A carbon atom can and does form four bonds, which is among the reasons why orbital hybridization proved to be such a successful theory.

Neutral carbon is located in group 14, period 2 of the periodic table and has an atomic number of 6 and, subsequently, a total of 6 electrons.

Out of these six electrons, it has, four are its valence electrons, i. e the electrons located in the outermost shell of the atom. 

Notice that out of the 4 valence electrons a carbon atom has, only 2 are unpaired and thus available for bonding, the ones located in the 2px and 2py orbitals. So, in theory, carbon should not be able to form four bonds since that would require 4 unpaired electrons, not 2.

Here's where orbital hybridization came into play. According to this theory, when the carbon atom is in an excited state, one of the two electrons located in the 2sorbital will get promoted to the empty 2pz orbital.

Then the 2s and the three 2p orbitals will combine to form four sp3 hybrid orbitals, 

As a result, carbon now has 4 unpaired valence electrons with which it can form four bonds.

Answer 2

it could gain 4 electrons forming c^4- anion.but it could be difficult for 6 protons to hold on ten electrons,that is 4 extra electron

it could lose 4 electrons forming c^4+cation.but it would require a large amount of energy to remove 4 electrons leaving behind a carbon cation with 6 protons in its nucleus holding on to just two electrons