Euler's theorem 2

$3333^{4444} \pmod{100} \equiv 33^4 \pmod{100}$

Because $\gcd(3333, 100) = 1$ and $\phi(100) = 40$

Now just expand $33^4$ like $(30 + 3)^4$

So our ans is just $(\binom{4}{3} \cdot 30 \cdot 3^3 + \binom{4}{4} \cdot 3^4) \pmod{100} \equiv 3321 \pmod{100} = 21$