correct answer is: c) 3 : 8

Explanation

Here,
x\ :\ y=6\ ∶\ 11
\rightarrow\frac{x}{y}=\frac{6}{11}
\rightarrow11x=6y _{[cross multiply]}
\rightarrow x=\frac{6y}{11}
Now,
\left(8x-3y\right):\left(3x+2y\right)
\rightarrow\left(8\times\frac{6y}{11}-3y\right)\ ∶\ \left(3\times\frac{6y}{11}+2y\right) _{[put the value ‘x’]}
\rightarrow\left(\frac{48y}{11}-3y\right)\ ∶\ \left(\frac{18y}{11}+2y\right)
\rightarrow\left(\frac{48y-33y}{11}\right)\ ∶\ \left(\frac{18y+22y}{11}\right)
\rightarrow\ \frac{15y}{11}\ ∶\ \frac{40y}{11}
\rightarrow\frac{15y}{11}\div\ \frac{40y}{11}
\rightarrow\ \frac{15y}{11}\times\frac{11}{40y}
\rightarrow\frac{3}{8}
\rightarrow\ 3\ ∶\ 8
Ans: 3 : 8