Solution:
Given, 2^a = 3^b = (12)^c

We need to find the value of 1/c - 1/b - 2/a

Let's try to simplify the given expression step by step.

Step 1:
As 2^a = 3^b, we can write 2^a = (2^log2(3))^b
=> 2^a = 2^(b*log2(3))
=> a = b*log2(3) ----(1)

Step 2:
As 3^b = (12)^c, we can write 3^b = (3*4)^c
=> 3^b = 3^c*4^c
=> 3^b = (3^c)*(2^2c)
=> b = c + 2c*log2(2)
=> b = 3c ----(2)

Step 3:
Substituting the values of a and b from (1) and (2), we get
a = 3c*log2(3) ----(3)

Step 4:
Now, substituting the value of b from (2) in (1), we get
a = 3(c*log2(3))/log2(3)
=> a = 3c ----(4)

Step 5:
Substituting the value of a from (4) in (3), we get
a = 3c*log2(3)
=> log2(3^a) = 3c*log2(3)
=> 3^a = 2^(3c*log2(3))
=> 3^a = (2^log2(3))^3c
=> 3^a = 3^3c
=> a = 3c ----(5)

From (4) and (5), we can conclude that a = b = c.

Step 6:
Substituting the values of a, b, and c in the expression 1/c - 1/b - 2/a, we get
1/c - 1/b - 2/a = 1/a - 1/a - 2/a
=> 1/c - 1/b - 2/a = -1/a
=> 1/c - 1/b - 2/a = -1/3c

Therefore, 1/c - 1/b - 2/a reduces to -1/3c.

Conclusion:
Hence, the value of 1/c - 1/b - 2/a is -1/3c.