[aruanan]

But 12 + 34 x 56 + 78 + 9 = 2003 requires that the multiplication be done before the addition operations. So which is it, left to right or multiplication first?

Multiplication and division over addition and subtraction. A "puzzle" that depends on violating order of operations isn't really a puzzle.

[KarlInOhio]

Well, I went through all 390625 possible combinations of operators or their absence between the nine digits. Three came up with the right result (and two more had the "right" result, but only because the program I used rounded down fractional results) , but only one had three operators.

Highlight the following line to see the result.

1234-5-6+789=2012
The order of operations never came up because there is no multiplication.

End of answer.