The measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8

Let x be the unknown angle. 

Make an equation using the formula.

"measure of one acute angle is 3 times" Since we know that x is the one acute angle, we can multiply that by 3 to get 3x.

"the sum of" when ever you see the word 'sum' it means that there will be an addition process involved and in this case it also means that 3x will equal to the rest of the equation. (3x=)

"measure of the other acute angle and 8" We already know that the other angle is x . Since there is no other indicator of the 8 being subtracted, multiplied, and divided and that we know this is an addition problem, we can conclude that 8 will be added to the other angle. (x+8)

So, now we have the equation and all we have to do is simplify it. 

3x= x+8
-x   -x             *Move constants and variables to opposite sides*

2x=8
---  ---             *Divide by 2 to isolate the variable* 
2    2

x=4

So, I'm assuming you want to know the measure of both angles. All you have to do is plug in the x in the 3x and x+8 depending on which angle you want.

3x
3(4)=12
The measure of the first angle is 12.

x+8
4+8= 12
The measure of the second angle is also 12.