To solve this expression, we first simplify each part separately:

(7/15 + 3/10) * 2:

To add the fractions, we need to find a common denominator, which is 30.
7/15 = 14/30
3/10 = 9/30Now we add them: (14/30 + 9/30) = 23/30Finally, multiply by 2: 23/30 * 2 = 46/30 = 23/15

14/23 + 1 6/57:

Convert the mixed number to an improper fraction:
1 6/57 = (1 * 57 + 6) / 57 = 63/57Add the fractions: 14/23 + 63/57 = (1457 + 6323) / (23*57) = (798 + 1453) / 1311 = 2251 / 1311

(30/57 - 3/19):

To subtract the fractions, we need to find a common denominator, which is 57.
30/57 = 30/57
3/19 = (3 3) / (19 3) = 9/57Now we subtract them: 30/57 - 9/57 = 21/57 = 7/19

Putting it all together:

((23/15) + (2251/1311)) : (7/19) = ((23/15) + (2251/1311)) (19/7)
= ((237 + 225115) / (151311)) (19/7)
= ((161 + 33765) / 19665) (19/7)
= (33926 / 19665) * 19/7)
= 1.726rPidSo, the final answer is approximately 1.726.