What is the basis for designating `C_(3)` and `C_(4)` pathways of photosynthesis ?

Explanation

`C_3` pathway is also called Calvin cycle. It represents the dark phase. Here `CO_2` is accepted by Ribulose diphosphate (RuDP) a 5-C pentose sugar and first product of CO, fixation is 3-C substance i.e. 3 phosphoglyceric acid.
In `C_4` pathway `CO_2` is first accepted by 3-C substance i.e. phosphoenol pyruvate (PEP) and it forms oxaloacetic acid (4-Carbon).