Which figure represents the image of parallelogram lmnp after a reflection across the line y=x

You haven't provided the parallelogram , therefore, I cannot give an exact answer.
However, I will help you with the concept.

When reflecting a point across the line y = x:
We swap the values of x and y while keeping their sign the same.

This means that:
(x,y) > reflection across y = x > (y,x)

Examples:
(2,3) > reflection across y = x > (3,2)
(1,-4) > reflection across y = x > (-4,1)
(-3,6) > reflection across y = x > (6,-3)
(-5,-7) > reflection across y = x > (-7,-5)

Based on the above, all you have to do is get each point of the parallelogram and swap its x and y coordinates to get its image when reflected across y = x

Hope this helps :)