Solution:

Given: 2/3A = 4/5B = 1/6C

To find: A : B : C

To solve this problem, we can use the concept of proportions. We are given three ratios: 2/3A, 4/5B, and 1/6C. We can set up the proportions as follows:

2/3A = 4/5B = 1/6C

Let's solve for A, B, and C separately.

Solving for A:
We have the ratio 2/3A. To isolate A, we can cross multiply and solve for A.

Cross multiplying, we get:
2 * A = 3 * 1
2A = 3
A = 3/2

Solving for B:
We have the ratio 4/5B. To isolate B, we can cross multiply and solve for B.

Cross multiplying, we get:
4 * B = 5 * 1
4B = 5
B = 5/4

Solving for C:
We have the ratio 1/6C. To isolate C, we can cross multiply and solve for C.

Cross multiplying, we get:
1 * C = 6 * 1
C = 6

Therefore, A = 3/2, B = 5/4, and C = 6.

A : B : C = 3/2 : 5/4 : 6

To simplify the ratio, we can convert the fractions to a common denominator.

LCM of 2 and 4 is 4. So, we multiply the first fraction by 2/2 and the second fraction by 4/4.

A : B : C = (3/2) * (2/2) : (5/4) * (4/4) : 6
A : B : C = 6/4 : 20/16 : 6
A : B : C = 3/2 : 5/4 : 6

Therefore, the ratio A : B : C is 3/2 : 5/4 : 6.

In conclusion, the ratio A : B : C is 3/2 : 5/4 : 6.