78 B.
$$
f(a)=(a+1)(a+2) .
$$

From $3 \mid f(a)$ we get
$$
a \equiv 1,2(\bmod 3) .
$$

It is easy to see that
$$
a \equiv 2(\bmod 3)
$$

has 33 solutions, and
$$
a \equiv 1(\bmod 3)
$$

has 34 solutions, for a total of 67. These are the solutions we seek.
78 Let $f(x)=x^{2}+3 x+2$, and $S=\{0,1,2,3, \cdots, 100\}$, if $a \in S$ and $f(a)$ is divisible by 6, the number of such $a$ is
A. 69
B. 67
C. 66
D. 34