Applying similar figures, the required sides are
CB = 4.5
DA = 4.5
XY = 9
CD = 4
Perimeter of ABCD = 19
Perimeter of WXYZ = 38
How to find the required sides
The required sides is solved using proportions derived from similar figures.
The proportion includes
AB / XW = CB / ZW
Where DA = CB and ZW = XY
Solving for CB
AB / WX = CB / ZW
6 / 12 = CB / 9
CB = 9 * 1/2 = 4.5
CB = DA = 4.5
ZW = XY = 9
Solving for CD
AB / WX = CD / YZ
6 / 12 = CD / 8
CD = 8 * 6/12 = 4
Perimeter of ABCD
= AB + CD + AD + BC
= 6 + 4 + 4.5 + 4.5
= 19
Perimeter of WXYZ
= WX + YZ + XY + ZW
= 12 + 8 + 9 + 9
= 38