This was quite fun to solve.
I am not going to do the whole thing for you but I will give you a good outline.
I put a letter in each of the boxes
a,b,c in the top row
d,e,f in the second row
g,h,i in the bottom row.
Now I looked just at the solutions for a
a=1/3(a+b+c) and a=3/4(a+d+g)
by simplifying these and looking at possible solutions
I determined the value for a, d and g
and that b+c =12 which meant that both b and c had to be between 3 and 9. And c=12-b
I redrew the boxes with all the info that I just gleaned.
Next I looked at the two equations for e and from those I get the value of e and f and I found that h=4-b
Last I looked at the equations for i and finished the problem.
Finally I checked my answers and they all worked.