1. **State the problem:** Determine if the equation $2x + 8 = 2(x + 4)$ has infinite solutions or no solutions. 2. **Recall from previous solution:** We simplified the equation to $8 = 8$ after canceling terms involving $x$. 3. **Interpret the result:** Since the simplified equation is a true statement independent of $x$, it means the original equation holds for all values of $x$. 4. **Conclusion:** The equation has infinitely many solutions because it is true for every real number $x$. **Final answer:** The equation has infinite solutions.