To solve this, we will first convert all mixed numbers to improper fractions.

2 12/17 = (2 17 + 12) / 17 = 46/17
4 5/17 = (4 17 + 5) / 17 = 73/17
6 4/5 = (6 5 + 4) / 5 = 34/5
5 3/5 = (5 5 + 3) / 5 = 28/5

Now let's substitute these values back into the equation:

(46/17 + 73/17) - (34/5 + 28/5) ÷ 3

Now add the fractions within the parentheses:

(46/17 + 73/17) = 119/17
(34/5 + 28/5) = 62/5

Now, subtract the fractions outside of the parentheses:

119/17 - 62/5

To subtract fractions, we must have the same denominator:

To find a common denominator between 17 and 5, multiply them together:
17 * 5 = 85

Now rewrite the fractions with the common denominator:

(119/17 5/5) - (62/5 17/17)
= (595/85) - (1054/85)

Now subtract the fractions:

595/85 - 1054/85 = -459/85

Finally, divide the result by 3:

-459/85 ÷ 3 = -153/85

Therefore, the simplified answer is -153/85.