To solve this problem, we will follow the order of operations (PEMDAS):

Parentheses:
We will first simplify the terms inside the parentheses:
-7 + 3 = -4
Therefore, the expression becomes:
340 - 72/(-4) - (-6)

Division:
Now, we will perform the division operation:
72 / (-4) = -18
Now, the expression becomes:
340 - (-18) - (-6)

Subtraction:
Next, we will simplify the subtraction:
-(-18) = 18
-(-6) = 6
Now, the expression becomes:
340 - 18 + 6

Addition:
Finally, we will perform the addition operation:
340 - 18 + 6 = 328

Therefore, the solution to the expression 340 - 72/(-7+3) - (-6) is:
328.