Here, we add both integral and fractional part separately and follow the order of BODMAS.

$$\begin{gathered} = 4+\frac{1}{2}-\left(2+\frac{5}{6}\right)+1+\frac{7}{12}=? \\ = (4-2+1)+\left(\frac{-5}{6}+\frac{7}{12}+\frac{1}{2}\right)=? \\ = ? =3+\left(\frac{-10+7+6}{12}\right)=3+\frac{1}{4}=\frac{13}{4} \\ = 3\frac{1}{4} \end{gathered}$$

Hence, Option A is correct.