B is between A and C. If AB = 4, BC=2x+6 and AC= 1/2X +24. Find the length of BC and AC

I assume you mean 0.5 x and not 1/(2x)

Use Parentheses !!!!
4 + 2 x + 6 = .5 x + 24
1.5 x + 10 = 24
1.5 x = 14
3 x = 28
x = 28/3 etc