As I see, there are $960$ solutions ($80$ different solutions, ignoring rotation and mirror-transformation).
For example, $2$ of them:
Way of solving: "try-and-check".
Consider any values $a,h$.
For example, $a=5,h=6$.
Then possible values for $i,c$ are:
For these values you'll get system of $5$ equations for $8$ variables. Reduction of system.
Sometimes such system will have no solutions.
Consider $3$ any values for cells $a,c,e$.
Choose values for $b,d,f$, such that $a+c+e=b+d+f$.
When we'll have values for $a,b,c,d,e,f$, we'll get system of $6$ equations for $6$ variables ($g,h,i,j,k,l$).
But such system can have no solutions.
If you'll use brute computer search, then there is not so much permutations of $12$ numbers: $12! = 479~001~600$ (a few seconds of computer work).