The sum of three numbers is 78. the second number is 2 times the third. the third number is 6 more than the first. what are the numbers?

X+y+z=78
   y     =2z
z=x+6

We can express x and y from 2nd and 3d equations, and substitute their values into the 1st.

y = 2z and x= z-6

x+y+z=78
z-6+2z+z=78
4z -6 =78
4z= 84
z=21

 y =2z ,   y=2*21,   y=42

x= z-6, x= 21-6,  x=15

x=15, y=42, z=21.

Check:
15+42+21 = 78
78=78