A student solved the following equation using the following steps:

The student's work shows that the equation was solved **correctly**.

Let's analyze the given equation and the steps taken:

1. The equation starts as:
\[
2(2x + 2) = 4(x + 4)
\]

2. Distributing both sides:
- Left side: \(2(2x) + 2(2) = 4x + 4\)
- Right side: \(4(x) + 4(4) = 4x + 16\)

So the equation becomes:
\[
4x + 4 = 4x + 16
\]

3. Simplifying it:
- Subtract \(4x\) from both sides, which gives:
\[
4 = 16
\]

However, this statement is false.

Essentially, an equation that simplifies to a false statement indicates that there are **no solutions** to the equation, not infinitely many.

In conclusion, the final result \(4 = 4\) as derived by the student from the distribution step is misleading in this context because it suggests that there are infinitely many solutions. To clarify, the equation does not have \(4 = 4\) from the steps provided, but instead, leads to a false equality from which we conclude that there are no solutions.

So, the correct answer is:
The equation was solved **incorrectly**, indicating it has **no solutions**.