1. **State the problem:** We are given the equation $$f = \frac{b^2 + w}{2 - b}$$ and need to find the value of $w$ when $b = 4$ and $f = -10$. 2. **Write down the formula:** $$f = \frac{b^2 + w}{2 - b}$$ 3. **Substitute the known values:** Replace $f$ with $-10$ and $b$ with $4$: $$-10 = \frac{4^2 + w}{2 - 4}$$ 4. **Simplify the denominator and numerator:** $$-10 = \frac{16 + w}{-2}$$ 5. **Multiply both sides by the denominator to isolate the numerator:** $$-10 \times \cancel{-2} = (16 + w) \times \cancel{-2}$$ $$20 = 16 + w$$ 6. **Solve for $w$ by subtracting 16 from both sides:** $$20 - 16 = w$$ $$w = 4$$ **Final answer:** $$w = 4$$