To solve this problem, we will first perform the multiplications and then subtract the result from 2/3.

Multiplying the fractions:

2 1/3 1 4/7 = (6/3 + 1) (7/7 + 4/7) = 7/3 * 11/7 = 77/21

1 4/11 1 4/15 = (11/11 + 4/11) (15/15 + 4/15) = 15/11 * 19/15 = 285/165

Now, multiply the above result with 4/19:

77/21 285/165 = 1001/231 285/165 = 285285/38115 = 95/127

Now, subtract 2/3 from the above result:

95/127 - 2/3 = (953 - 1272) / (127*3) = (285 - 254) / 381 = 31 / 381

Therefore, the result of the calculation 2 1/31 4/71 4/111 4/151 4/19 - 2/3 is 31/381.