Help plz and explain

Short Answer: Sin(A) = 0.6
Givens
DE = 6
BD = 8
C and E are right angles.
ABD are colinear
AB is the hypotenuse of Triangle ACB
BD is the hypotenuse of Triangle BED

Discussion
BC is parallel to DE. Two lines that lie on the same transversal have the same slope as the transversal. The slope can be measured as rise over run for all 3 segments (AB, BD and AD) Since the right angles describe the slope for AB and BD, BC is parallel to DE.

By corresponding angles, <ABC is equal to <BDE and by the AA (angle angle theorem) the triangles containing these two angles are similar.

The first part of this discussion is a little shaky, but it is essentially correct.

Step One
Find BD
You are correct. It is 10.

Step two
Using the similarity process, find the ratio between BD and AB
BD:AB = 10:18
BD:AB = 5:9

Step Three
Use this ratio to find BC (we will discuss the shorter way below)

5/9 = DE/BC
5/9 = 6/x Cross multiply
5x = 9*6
5x = 54
x = 54/5
x = 10.8

BC = 10.8

Step four
find the Sin(A)
Sin(A) = opposite / hypotenuse
Sin(A) = 10.8 / 18
Sin(A) = 0.6

Shorter method
Since the two triangles are similar <A = <DBE
Sin(<DBE) = 6/10
Sin(<DBE) = 0.6

Answer: Sin(A) = 0.6 <<<<<<