\(\dfrac{3}{2}-\dfrac{5}{6}\div\left(\dfrac{1}{2}\right)^2+\sqrt{4}\)
\(=\dfrac{3}{2}-\dfrac{5}{6}\div\dfrac{1}{4}+2\) \(=\dfrac{3}{2}-\dfrac{5}{6}\cdot4+2\) \(=\dfrac{3}{2}-\dfrac{10}{3}+2\)
\(=\dfrac{9}{6}-\dfrac{20}{6}+2=\dfrac{-11}{6}+2=\dfrac{-11}{6}+\dfrac{12}{6}=\dfrac{1}{6}\)