What is effective capacitance between points X and Y ?

This circuit is redrawn and is shown in fig. This is a case of balanced Wheatstone bridge. Capacitance C' between ABD
 

$\frac{1}{{\mathrm{C}}^{\mathrm{\prime }}}=\frac{1}{{\mathrm{C}}_1}+\frac{1}{{\mathrm{C}}_2}=\frac{1}{3}\text{ or }{\mathrm{C}}^{\mathrm{\prime }}=3\mathrm{\mu F}$
Capacitance C" between ACD
$\frac{1}{{\mathrm{C}}^{\prime \prime }}=\frac{1}{{\mathrm{C}}_3}+\frac{1}{{\mathrm{C}}_4}=\frac{1}{3}\text{ or }{\mathrm{C}}^{\prime \prime }=3\mathrm{\mu F}$
Capacitance between X and Y
$\mathrm{C}={\mathrm{C}}^{\mathrm{\prime }}+{\mathrm{C}}^{\prime \prime }=3\mathrm{\mu F}+3\mathrm{\mu F}=6\mathrm{\mu F}$.