To find: The value of measure LM.

Given:
The given figure is as follows.

Calculation:
As shown in the figure ${\displaystyle \overline{JM}\stackrel{\sim }{=}\overline{JL}}$.
From the Reflexive Property of congruence, ${\displaystyle \overline{JF}\stackrel{\sim }{=}\overline{JF}}$.
The ${\displaystyle \mathrm{\angle }JFM}$, and ${\displaystyle \mathrm{\angle }JFL}$ right anges because ${\displaystyle \overline{JF}perp\overline{ML}}$.
From the HL congruence, ${\displaystyle \mathrm{△}JFM\stackrel{\sim }{=}\mathrm{△}JFL}$.
In congruent triangles, corresponding elemnts are congruent so ${\displaystyle \overline{MF}\stackrel{\sim }{=}\overline{LF}}$.
From the definition of congruent segments MF =LF =6.
From the segment Addition Postulate,
LM=MF+LF
=6+6
=12
Therefore, the value of measure LM is 12.