Question

What is the total number of valence electrons in a carbon atom in the ground state

Answer 1

Carbon will have 4 valence electrons.  It will have 2 in the p orbital and 2 in the s orbital.  You can see this when you find the noble gas configuration of carbon which is [He]2s²2p² showing that carbon has 4 valence electrons.
I hope this helps.  Let me know if anything is unclear.