Three times the sum of a number and 4 is 8 less than one-half the number. write and solve an equation to find the number.

3(x+4)=1/2x-8  that's your original equation. If you read through the problem as you look at my work, you will see it matches up as you read it out loud and see my equation. 
to solve, first distribute.
3x+12=1/2x-8 
next you need to subtract 1/2x from both sides. this is using the identity property of addition. 
2.5x+12=-8
next, subtract 12 from both sides. this demonstrates the identity property of subtraction.
2.5x=-20
next, divide by the coefficient of x (which is 2.5) to find the value of x, your variable.
x=8. you're done. hope this helped :)