Question
$$\frac{2x+6}{2}-x = 3$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} \frac{2x+6}{2}-x &= 3&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{2x+6}{2}-2x &= 2\cdot3&& \text{cancel out the denominators} \\[1 em]2x+6-2x &= 6&& \text{simplify left side} \\[1 em]2x+6-2x &= 6&& \\[1 em]6 &= 6&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 6 = 6 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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