\(C _1=\frac{\epsilon_0 A }{\left(\frac{ d / 3}{ k }+\frac{2 d }{3}\right)}=\frac{\epsilon_0 A }{\frac{ d }{12}+\frac{2 d }{3}}\)

\(=\frac{\epsilon_0 A }{ d } \times\left(\frac{12}{9}\right)\)

\(C _1=\frac{4}{3} \frac{\epsilon_0 A }{ d }=2 \mu F\)

\(\text { for } x =\frac{2 d }{3}\)

\(C _2=\frac{\epsilon_0 A }{\left(\frac{2 d / 3}{ k }+\frac{ d }{3}\right)}=\frac{\epsilon_0 A }{ d } \times 2\)

\(\Rightarrow \frac{6}{4} \times 2=3 \mu F\)