jmc

When we are subtracting, we want to subtract a smaller number from a bigger number. We can pull out a negative sign in order to accomplish this: $$35_8-74_8=-(74_8-35_8).$$Now, we can line in the numbers and subtract just as we do in base 10. For example, when we borrow from the $8^1$s place, the digit 1 in the units place becomes $4+8=12$, while the digit in the $8^1$s place decreases by 1. Continuing in this way, we find \begin{array}{c@{}c@{}c@{}c} & & \cancelto{6}{7} & \cancelto{12}{4}_8 \\ & - & 3 & 5_8 \\ \cline{2-4} & & 3 & 7_8 \\ \end{array}Therefore, $35_8-74_8=-(74_8-35_8)=\boxed{-37_8}$.