Angle ABC = angle DBE since they are angles that perfectly overlap, or they are shared common angles.
Angle BED = angle BCA because of the tick marks on the angle drawing.
By the AA (angle angle) similarity theorem, the two triangles ABC and DBE are similar.
Because they are similar, we can form the proportion below and solve for x
BC/BE = AC/DE
(28+x)/28 = 48/32
32*(28+x) = 48*28
896+32x = 1344
32x = 1344-896
32x = 448
x = 448/32
x = 14
Now that we know x, we can find BC
BC = 28+x
BC = 28+14
BC = 42
Final Answer: 42