You have the correct idea. You need to divide the $3000 into 2 parts and apply 10% to one part and 8% to the other. If you only knew one part you could find the other since the sum is $3000. This is a place where the notation of algebra really helps.
Suppose that $x was invested at 10% them $(3000 - x) was invested at 8%.
In one year, $x invested at 10% would yield an interest of 0.10 x.
In one year, $(3000 - x) invested at 8% would yield an interest of 0.08 (3000 - x).
But you know that the total interest is $256 and hence
0.10 x + 0.08 (3000 - x) = 256
Solve for x.