To find the unit digit of $6^{129}$, we note the unit digit of powers of 6 is always 6. For $7^{307}$, the unit digits cycle every 4 terms: $7, 9, 3, 1$; $307 \mod 4 = 3$, so the unit digit is 3. Multiplying the unit digits: $6 \times 3 = 18$, thus the unit digit is 8.