To solve this problem, we need to find a common denominator for all the fractions. The least common multiple of 3, 6, 9, 12, and 15 is 180.

Converting each fraction to have a denominator of 180:

2/3 = (2/3) * (60/60) = 120/180
4/6 = (4/6) * (30/30) = 80/180
6/9 = (6/9) * (20/20) = 40/180
8/12 = (8/12) * (15/15) = 40/180
10/15 = (10/15) * (12/12) = 80/180
12/18 = (12/18) * (10/10) = 120/180

Now, we can add the fractions:

120/180 + 80/180 + 40/180 + 40/180 + 80/180 + 120/180

Adding the numerators:

(120 + 80 + 40 + 40 + 80 + 120)/180

Adding the numerators:

480/180

Simplifying the fraction:

480 ÷ 180 = 8/3

Therefore, 2/3 + 4/6 + 6/9 + 8/12 + 10/15 + 12/18 = 8/3.