So line PQR is parall4el to the horizontal bottom side AD.

"Points P and Q are symmetric about line AB ...."

That means P and Q are equidistant from vertical side AB.

"....and points Q and R are symmetric about line CD."

Likewise, Q and R are equidistant from the vertical side CD.

Let point Q be anywhere inside the rectangle ABCD.

Say, Q is x away from AB.

Hence, Q is (4 -x) away from CD.

Then P is x away from AB, and R is (4 -x) away from CD.

So, for the total length of line PQR,

PR = x +x +(4 -x) +(4 -x) = 8 --------------answer.