$$\left(\dfrac{1}{4}\times \dfrac{1}{4}\right)+\left(\dfrac{1}{2}\times 6\right)$$
$$=\left(\dfrac{1}{4}\times \dfrac{1}{4}\right)+\left(\dfrac{1}{2}\times 6\right)$$
$$=\dfrac{1}{8}+\dfrac{6}{2}$$
$$=\dfrac{1+24}{8}$$
$$=\dfrac{25}{8}$$
Therefore, the reciprocal is $$\dfrac{8}{25}$$