In a little more detail, the surface of this cylinder consists of two disk with diameter equal to the diameter of the cylinder and the cylindrical "side".
The area of a disk with diameter 4x+ 2 (so radius 2x+ 1) is \(\displaystyle \pi(2x+ 1)^2\) so the area of the top and bottom is \(\displaystyle 2\pi(2x+ 1)^2\).
To find the area of the side, imagine cutting it vertically and opening it out to form a rectangle. The width of that rectangle is the height of the cylinder, 2x. The length is what previously was the circumference of the cylinder, \(\displaystyle \pi\) time the diameter, \(\displaystyle \pi (4x+ 2)\). So the total surface area is \(\displaystyle 2\pi(2x+ 1)^2+ \pi(4x+ 2)\).