$$2 \dfrac{5}{8} - 2 \dfrac{1}{6} + 4 \dfrac{3}{4}$$
It can be written as
$$= 21/8 - 13/6 + 18/4$$
Here the LCM of $$8, 6$$ and $$4$$ is $$24$$
$$= \left (21 \times 3 \right )/ \left (8 \times 3 \right ) - \left (13 \times 4 \right )/ \left (6 \times 4 \right ) - \left (19 \times 6 \right )/ \left (4 \times 6 \right )$$
By further calculation
$$= 63/24 - 52/24 + 114/24$$
So we get
= $$\left (63 - 52 + 114 \right )/24$$
= $$\left (117 - 52 \right )/12$$
$$= 125/24$$
$$= 5 \dfrac{5}{24}$$