Rs=8y+4,st=4y+8,andrt=15y-9
what is the value of y
find rs, st, and rt

Even though you haven't bothered to explain it, or to attach a picture,
I'm going to assume that 'R' and 'T' are the ends, and in order to go
from 'R' to 'T', it's necessary to pass through 'S'.

If that's true, then        RS + ST = RT .

Knowing that, we can say that     (8y + 4) + (4y + 8) = 15y - 9

Remove parentheses:      8y + 4 + 4y + 8 = 15y - 9

Combine terms that are alike:    12y + 12 = 15y - 9

Subtract  12y  from each side:             12 = 3y - 9

Add  9  to each side:                            21 = 3y

Divide each side by  3  :          7 = y

RS = 8y + 4 = 56 + 4 = 60

ST = 4y + 8 = 28 + 8 = 36

RT = 15y - 9 = 105 - 9 = 96

Check:  RS + ST = 60 + 36 = 96 = RT       yay !