$$\begin{aligned} & 428=21 \times 20+8 \\ \Rightarrow \quad & (428)^{2024} \equiv(20 \times 21+8)^{2024} \equiv 8^{2024}(\bmod 21) \\ & 8^2=21 \times 3+1 \\ & 8^{2024}=(21 \times 3+1)^{1012} \\ \Rightarrow \quad & 8^{2024} \equiv(21 \times 3+1)^{1012}(\bmod 21) \\ & \equiv 1^{2012}(\bmod 21) \\ & 428^{2024} \equiv 1(\bmod 21) \end{aligned}$$