Answer is as follows:
∠BCA = 68
Segment BC = 8
∠DEF = 68
Segment DF = 24
Segment FE = 24
Step by step
Triangle ABC
Two known angles are 68 and 44, third angle can be found subtracting from 180 as all angles sum is 180.
180 - 68 - 44 = 68
Now we know this is an isosceles triangle with two equal angles of 68, and the two side lengths are congruent, measure of 8.
Now we can find measurements of triangle #2. Triangle #2 has the same angle measurements as ABC, and angle B is congruent to angle F, thus triangle #2 is labeled DFE.
To find the side lengths of DFE, we will find the ratio from side AC (6) that is similar to DE (18). 18:6 ratio or 18/6 = multiply (dilation) x 3 from ABC to DFE.
Side AB = 8, multiply by the rate of 3 to find side DF = 24. Side AB is congruent with BC so side DF is congruent with side FE, so FE = 24. All angles and sides are found.