Answer     16

$$\begin{array}{rl} 8^{88}\equiv & 2^{264} \\ \equiv & \left(2^{10}\right)^{26}\times 2^4 \\ \equiv & 24^{26}\times 16\\ \equiv & 76^{13}\times 16\\ \equiv & 76\times 16\\ \equiv& \boxed{16}\pmod{100} \end{array}$$