1. **State the problem:** We need to find the number $x$ such that four times the sum of the number plus 2 equals eight times the number minus 28. 2. **Write the equation:** The problem translates to the equation $$4(x + 2) = 8x - 28$$ 3. **Expand the left side:** $$4x + 8 = 8x - 28$$ 4. **Bring all terms involving $x$ to one side and constants to the other:** Subtract $4x$ from both sides: $$\cancel{4x} + 8 = 8x - 28 - \cancel{4x}$$ which simplifies to $$8 = 4x - 28$$ 5. **Add 28 to both sides:** $$8 + 28 = 4x - 28 + 28$$ $$36 = 4x$$ 6. **Divide both sides by 4 to solve for $x$:** $$\frac{36}{\cancel{4}} = \frac{4x}{\cancel{4}}$$ $$9 = x$$ 7. **Conclusion:** The number is $9$. **Final answer:** $9$