SOLUTION :
Let the number of cocks $=x$
$\&$ the number of goats $=y$
$\therefore$ From the question,
$x+y=76$
$2 x+4 y=212$
$\therefore \quad$ We get after solving eqn. (i) and (ii), $x=46$, and $y=30$.
$\therefore$ Total no. of cocks $=46$; Ans.
$\therefore$ Correct option is $(c)$
TRICK : Suppose that the all heads are of goat.
$\therefore \quad$ Number of legs $=76 \times 4=304$
Difference of their feet
$=304-212=92$
The difference of their feet
$=4-2=2$
No. of cocks $=\frac{92}{2}=46 ;$ Ans.