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.