1. **State the problem:** Solve for $s$ in the equation $$\frac{s - 37}{-8} = -6.$$\n\n2. **Formula and rules:** To solve for $s$, we need to isolate $s$ on one side. Since $s$ is in the numerator divided by $-8$, multiply both sides by $-8$ to cancel the denominator.\n\n3. **Multiply both sides by $-8$:**\n$$\cancel{-8} \times \frac{s - 37}{\cancel{-8}} = -6 \times (-8)$$\nwhich simplifies to\n$$s - 37 = 48.$$\n\n4. **Isolate $s$ by adding 37 to both sides:**\n$$s - 37 + 37 = 48 + 37$$\n$$s = 85.$$\n\n5. **Final answer:**\n$$s = 85.$$