$$4\cdot\frac{3}{2}-2 = 2\cdot\frac{3}{2}+1$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 4\cdot\frac{3}{2}-2 &= 2\cdot\frac{3}{2}+1&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot4\cdot\frac{3}{2}-2\cdot2 &= 2\cdot2\cdot\frac{3}{2}+2\cdot1&& \text{cancel out the denominators} \\[1 em]12-4 &= 6+2&& \text{simplify left and right hand side} \\[1 em]8 &= 8&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 8 = 8 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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