Does anyone know how to do this

Can you explain clearly? I feel like I should know but I can't seem to grasp it.

http://i51.tinypic.com/2v0zvno.gif

Okay, so these two triangles are similar.
Their side lengths are proportional, so if AB equals 6 and ED equals 10, the rest of the sidelengths must also correspond in a 6:10 ratio (aka 3:5)
Since you know BD is 24, you can write the equation 3x+5x=24, 3x being BC and 5x being CD.
8x=24
x=3
Just plug in that number to BC and CD (3x and 5x) and there's your answer

With the triangles being similar, the sides along the bottom split the 24-inch width in the same ratio as the ratio of the sides on either end. 6/10 of the 24 inches is on the right and 4/10 of the 24 inches is on the left.

This gives you two equations:

1) BC / DC = 6/10 which reduces to 3/5

2) BC + DC = 24

Multiply both sides of equation 1 by DC to get:

BC = (3/5)DC

Substitute that value into equation 2 for BC:

(3/5)DC + DC = 24

Multiply through by 5 to clear the

3DC + 5DC = 120

8DC = 120

DC = 120 / 8 = 15 inches

That makes BC 9 inches.