Irealy need
triangle abc is similar to triangle lmn by the aa similarity postulate.
also, m∠a = 108° and m∠c = 2(m∠m).
what is m∠m?
°

Since two of the triangles are similar that means they are the same thing : 
<A = <L
108 = 108

<C is twice from <M so :
<C is 2x                 < M is x             

as you note down the answer you can draw two triangles and label them according to thier values,  you will see that triangle ABC has two things now  ;
                                                           a = 108   and   c = 2x
when you have two measures in a triangle you can find the 3rd one :
suppose that third < of  triangle ABC is x ;
108 + 2x + x = 180
108 + 3x = 180
 3x = 180 - 108 
 3x = 72 
  x = 24
                
                                          <m = 24 

further if you want to find C :
                                          < c = 2x 
                                      < c = 2 ( 24 ) 
                                       < c = 48