1. **State the problem:** We need to find how many solutions the equation $d + 2 + 5d = 2 + 6d$ has. 2. **Write the equation:** $$d + 2 + 5d = 2 + 6d$$ 3. **Combine like terms on the left side:** $$6d + 2 = 2 + 6d$$ 4. **Subtract $6d$ from both sides:** $$\cancel{6d} + 2 = 2 + \cancel{6d}$$ $$2 = 2$$ 5. **Interpretation:** The variables cancel out and we are left with a true statement $2=2$, which means the equation is true for all values of $d$. **Final answer:** The equation has infinitely many solutions because it holds true for every value of $d$.