Describe the spin of carbon-14's valence electrons and explain how you came about your answer.

we have to know the spin of valence electrons of carbon-14

There are four unpaired electron which are called as valence electron also.The spin of the four unpaired electron is either upfilled or down filled.

The ground state electronic configuration of C-atom is 1s²2s²2p² and one electron from 2s orbital gets excited to 2p orbital. The elctronic configuration in excited state is 1s²2s¹2p³.  

The electron jumps because half-filled orbitals are more stable. Exchange energy is less than pairing energy.