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

Step 1: Apply the division in the first expression
(11, 1:3 2 1/6) = 11 / (1 + 3 + 2 1/6)
= 11 / (4 + 2 1/6)
= 11 / (4 + 13/6)
= 11 / (24/6 + 13/6)
= 11 / (37/6)
= 11 * 6 / 37
= 66 / 37
= 1 29/37

Step 2: Add the fractions in the first expression
1 2/21 + 1 29/37
= (1 + 2/21) + (1 + 29/37)
= 1 + 2/21 + 1 + 29/37
= 2 + 2/21 + 29/37
= 2 + (74/37) + (29/37)
= 2 + 103/37
= 2*37/37 + 103/37
= 74/37 + 103/37
= 177/37
= 4 29/37

Step 3: Multiply the result of the first expression by 3/4
(4 29/37) (3/4)
= (4 + 29/37) (3/4)
= (4 3) + (29/37 3)/4
= 12 + 87/37
= 12 21/37

Therefore, the final answer is 12 21/37.