elementary number theory - Calculate $2^{5104} bmod 10$ using mental arithmetic

I am practising interview for Jane Street's trader internship and I found the following question.

Question: Calculate $2^{5104} \bmod 10$ using mental arithmetic.

I know that $2^5 \bmod 10 \equiv 2 \bmod 10.$
So,

$$\begin{align*} 2^{5104} & = (2^5)^{1020} 2^4 \\ & \equiv 2^{1020}2^4 \\ & = (2^5)^{204}2^4 \\ & \equiv(2^5)^{40}2^8 \\ & \equiv (2^5)^8 2^8 \\ & \equiv (2^5)^3 2 \\ & \equiv 6 \bmod 10. \end{align*}$$

However, I find the calculations above very taxing if I use mental arithmetic. I believe there should be a faster way to answer the question but I am not able to find one.