If a number is multiplied by four, it gives the same result as 2/7 of 500 for. what is the number?

Sounds as tho you meant:

4n = (2/7)(500)
                                              1000
If that's the case, then 4n =
                                                 7
             1000         250
or n = =    (answer)
                28             7

Check:  does 4(250/7) equal (2/7)(500)?  YES.

DE is parallel to AC

DE = 2AC

Explanation

In triangle ABC, BD = AD

BE = EC

D is mid point of AB

E is the mid point of AC

According to the mid point theorem, ( The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”) DE is parallel to AC and equal to half of it