To determine how many solutions there are for the system of equations given by \( 3y = 3x + 6 \) and \( y = x + 2 \), we can start by simplifying the first equation.
The first equation \( 3y = 3x + 6 \) can be simplified by dividing every term by 3:
\[ y = x + 2 \]
Now we have two equations:
- \( y = x + 2 \)
- \( y = x + 2 \)
Both equations are identical, meaning they represent the same line. In terms of a system of equations, this indicates that every point on the line is a solution. Therefore, there are infinitely many solutions for this system of equations.
So, the answer is:
Infinitely many solutions.