In an arithmetic progression (A.P), the general formula for the \(n\)th term is given by:

\[a_n = a_1 + (n - 1)d\]

Where:

- \(a_n\) is the \(n\)th term

- \(a_1\) is the first term

- \(d\) is the common difference

Given that the 3rd term of the A.P is \(4x - 2y\) and the 9th term is \(10x - 8y\), we can set up two equations using the general formula:

For the 3rd term:

\[4x - 2y = a_1 + (3 - 1)d\]

\[4x - 2y = a_1 + 2d \quad \text{(Equation 1)}\]

For the 9th term:

\[10x - 8y = a_1 + (9 - 1)d\]

\[10x - 8y = a_1 + 8d \quad \text{(Equation 2)}\]

Now, we can solve this system of equations to find the values of \(a_1\) and \(d\).

Subtract Equation 1 from Equation 2:

\[10x - 8y - (4x - 2y) = 8d - 2d\]

\[6x - 6y = 6d\]

\[d = x - y\]

Therefore, the common difference of the arithmetic progression is \(x - y\).