Language is not regular bcoz we need to match count of $c$'s is equal to count of $b$'s $+$ count of $a$'s

and that can implement by **PDA.**

$\delta(q_0,a,\epsilon)= (q_0,a)$ [ push a in stack, as per language a comes first]

$\delta(q_0,a,a)= (q_0,aa)$ [push all $a$'s into stack]

$\delta(q_0,b,a) = (q_1,ba)$ [push $b$ in stack, state change to $q_1$ that sure b comes after $a$]

$\delta(q_1,b,b)=(q_1,bb)$ [push all $b$'s in stack]

$\delta(q_1,c,b) = (q_2,\epsilon)$ [ pop one $b$ for one $c$]

$\delta(q_2,c,b) = (q_2,\epsilon)$ [ pop one $b$'s for each $c$ and continue same ]

$\delta(q_2,c,a) = (q_3,\epsilon)$ [ pop one $a$ for one $c$ , when there is no more $b$ in stack]

$\delta(q_3,c,a) = (q_3,\epsilon)$ [pop one $a$ for each $c$ and continue same]

$\delta(q_3,\epsilon,\epsilon) = (q_f,\epsilon)$ [ if sum of $c$'s is sum of $a$'s and $b$'s then stack will be empty when there is no $c$ in input]

Answer is **option B** : language is context- free but not regular.

Note :1state changes make sure $b$'s comes after $a$ and $c$'s comes after $b$'s]