How can the number 39 be divided into two parts in order that the sum of 2/3 of one part and 3/4 of the other part is 28?

Answer 1

I will assume that by "divided" you mean split up, and not actual division

let one part be x, then the other is 39-x

so (2/3)x + (3/4)(39-x) = 28
times 12 , the LCD

8x + 9(39-x) = 336
8x + 351 - 9x = 336
-x = -15
x = 15

so parts are 15 and 24

check:
(2/3)(15) = 10
(3/4)(24) = 18 and their sum would be 28, as required

Answer 2

(2/3)x+(3/4)(39_x)=28
8x+9(39_x)/12=28
8x+9(39_x)=28 multiply by 12
8x+351_9x=336
_x=336_351
_x=_15
X=15