Let's solve the equation step by step.
The equation is:
\[ 5(2x + 2) - 4 = 2x + 6 \]
First, distribute the 5 on the left side:
\[ 10x + 10 - 4 = 2x + 6 \]
This simplifies to:
\[ 10x + 6 = 2x + 6 \]
Now, subtract \(2x\) from both sides:
\[ 10x - 2x + 6 = 6 \]
Which simplifies to:
\[ 8x + 6 = 6 \]
Next, subtract 6 from both sides:
\[ 8x = 0 \]
Now, divide by 8:
\[ x = 0 \]
So, we found one solution, \(x = 0\).
Conclusion:
The equation has one solution: \( x = 0 \).