AMC 12 Mock Exam 1 Problem 4

The units digits of $3^1,3^2,3^3,3^4,\dots$ are $3,9,7,1,\dots$ and repeat with period $4$; likewise for $7^1,7^2,\dots$ they are $7,9,3,1,\dots$. Since $2026\equiv 2\pmod 4$, the units digit of each of $3^{2026}$ and $7^{2026}$ is $9$. The sum ends in the units digit of $9+9=18$, namely $\boxed{8}$.