So, we know that ∠HIL = 118, and we also know that a line is 180 degrees. This means that ∠HIL +∠JIL = 180. We can use simple arithmetic and substitution to find that 180-118= 62, so ∠JIL = 62.
We have another line, Line N, so we know that the line is equal to 180 as well! Because ∠JIL and ∠ILM are both on this line, ∠JIL +∠ILM = 180. ∠JIL = 62, so 180 - 62 = 118.
Lastly, Line N is still equal to 180, so ∠ILM + ∠MLN = 180. In this case, we have 180-118=62, so ∠MLN = 62.
Or, using theorems, there is an easier way to do this.
The corresponding angles theorem tells us that "If a transversal intersects two parallel lines, the corresponding angles are congruent." So, we can see that both ∠MLN and ∠JIL are corresponding so they are congruent. First, however, we need to find ∠JIL, and if we look at our work from above, we see that ∠JIL = 62. Since ∠JIL and ∠MLN are congruent, or the same, ∠MLN is also 62.
:)