1. **State the problem:** Solve the equation $$0.1p - 0.2p + 2 = -4.6$$ 2. **Combine like terms:** $$0.1p - 0.2p = -0.1p$$ So the equation becomes: $$-0.1p + 2 = -4.6$$ 3. **Isolate the variable term:** Subtract 2 from both sides: $$-0.1p + 2 - 2 = -4.6 - 2$$ $$-0.1p = -6.6$$ 4. **Divide both sides by -0.1 to solve for $p$:** $$p = \frac{-6.6}{-0.1}$$ Show cancellation: $$p = \frac{\cancel{-6.6}}{\cancel{-0.1}}$$ 5. **Calculate the division:** $$p = 66$$ **Final answer:** $$p = 66$$