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$\left\{\left[\left(\dfrac{3}{4}-\dfrac{1}{2}\right)^2 : \left(\dfrac{1}{2}+\dfrac{1}{3}\right)+\dfrac{1}{2}\right] : \dfrac{69}{20}+1\right\}^2 : \dfrac{7}{12}=$

$= \left\{\left[\left(\dfrac{3-2}{4}\right)^2 : \left(\dfrac{3+2}{6}\right)+\dfrac{1}{2}\right]· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\left[\left(\dfrac{1}{4}\right)^2 : \dfrac{5}{6}+\dfrac{1}{2}\right]· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\left[\dfrac{1}{16}·\dfrac{6}{5}+\dfrac{1}{2}\right]· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\left[\dfrac{1}{\cancel{16}_8}·\dfrac{\cancel6^3}{5}+\dfrac{1}{2}\right]· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\left[\dfrac{1}{8}·\dfrac{3}{5}+\dfrac{1}{2}\right]· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\left[\dfrac{3}{40}+\dfrac{1}{2}\right]· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\left[\dfrac{3+20}{40}\right]· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\dfrac{23}{40}· \dfrac{20}{69}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\dfrac{\cancel{23}^1}{\cancel{40}_2}· \dfrac{\cancel{20}^1}{\cancel{69}_3}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\dfrac{1}{2}· \dfrac{1}{3}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\dfrac{1}{6}+1\right\}^2·\dfrac{12}{7}=$

$= \left\{\dfrac{1+6}{6}\right\}^2·\dfrac{12}{7}=$

$= \left\{\dfrac{7}{6}\right\}^2·\dfrac{12}{7}=$

$= \dfrac{49}{36}·\dfrac{12}{7}=$

$= \dfrac{\cancel{49}^7}{\cancel{36}_3}·\dfrac{\cancel{12}^1}{\cancel7_1}=$

$= \dfrac{7}{3}·\dfrac{1}{1}=$

$= \dfrac{7}{3}$