Units digit

Exponential Residues:

$6^n \cong 6 \cong 6^{15} \mod 10$

$7^{4n} \cong 1 \cong 7^4 \mod 10$

$9^{2n+1} \cong 9 \cong 9^3 \mod 10$

$6^{15} - 7^4 - 9^3 \cong 6 - 1 - 9 \cong 6 \mod 10$

$\begin{aligned} {\color{#3D99F6}6^{15}}-7^4 - 9^3 & \equiv {\color{#3D99F6}6}-(49)^2 - (10-1)^3 \text{ (mod 10)} & \small \color{#3D99F6} \text{Units digit of powers of 6 is always 6.} \\ & \equiv 6 - (50-1)^2 - (-1)^3 \text{ (mod 10)} \\ & \equiv 6 - (-1)^2 - (-1) \text{ (mod 10)}\\ & \equiv 6 - 1 +1 \text{ (mod 10)} \\ & \equiv \boxed{6} \text{ (mod 10)} \end{aligned}$