The short line on the sides of the triangle tells us that those sides are equal.
We can see that LN = NJ and
LO = KO
This means that triangle LNO is similar to triangle triangle LJK
LO/NO = (LO + OK)/JK
Given that NO = 16 and JK = 6x + 8, it means that
LO/16 = (LO + OK)/(6x + 8)
Since LO = OK, it means that
LO + OK = LO + LO = 2LO
Therefore
LO/16 = 2LO/(6x + 8)By cross multiplying, it becomes
LO(6x + 8) = 2LO * 16
LO(6x + 8) = 32LO
Dividing both sides of the equation by LO, it becomes
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 24/6
x = 4