The answer would be approximately 13.12.
As the triangles XYZ and KLJ are similar triangles, their sides will be in proportion. That means XY/KL = YZ/LJ = XZ/KJ.
So, 8.7/KL = 7.8/LJ = 8.2/13.92.
As we need length LJ, take equations
7.8/LJ = 8.2/13.92
LJ = (8.2 / 13.92) * 7.8
LJ = 13.12