The "perimeter" is the total distance around the rectangle. Imagine drawing a large rectangle on the ground and actually measuring the distances. There are, of course, 4 sides, 2 with length z and 2 with length z+ 4. You might first measure the length z, then the length z+ 4 and add them to get the length around those first two sides, then add the third side, another z, and finally, the fourth side, another z+ 4. The total distance is the sum of those: z+ z+4+ z+ z+ 4 which is also equal to 2z+ 2(z+ 4) or 4z+ 8.
Notice this does NOT involve multiplying two lengths together. That is
because "perimeter" is a distance measure. If the sides were measured in meters, then the perimeter is measured in distance also. If we multiplied two lengths together, the units would be " " or "square meters", an area measurement. In fact, the area of this rectangle is the product of the two side lengths, z(z+4), what you used for "perimeter".
I'm not sure how you got . Perhaps you were thinking of the area of a square, and were trying to do . But that, of course, ignores the length "z". And, if that was what you were trying to do, you multiplied wrong: .