To solve this expression, we follow the order of operations:

-6 + 6 + 4/5 + 1 2/3 + 3.4

First, we add -6 and 6 to get 0.

0 + 4/5 + 1 2/3 + 3.4

Next, we convert the mixed number 1 2/3 to an improper fraction. 1 2/3 = (1*3 + 2) / 3 = 5/3.

0 + 4/5 + 5/3 + 3.4

Now, we find a common denominator for the fractions.

0 + 12/15 + 25/15 + 3.4

Combine the fractions and the decimal.

0 + 37/15 + 3.4

Convert 37/15 to a mixed number. 37 ÷ 15 = 2 remainder 7. Therefore, 37/15 = 2 7/15.

0 + 2 7/15 + 3.4

Now, add the mixed number and the decimal.

2 7/15 + 3.4 = 2 + 3 + 7/15 + 0.4 = 5 + 7/15 + 0.4

Convert the decimal to a fraction: 0.4 = 4/10 = 2/5

5 + 7/15 + 2/5

Now, find a common denominator for the fractions.

5 + 7/15 + 6/15 = 5 + 13/15

Therefore, -6 + 6 + 4/5 + 1 2/3 + 3.4 equals 5 13/15.