Transposition Method to find the value of x:

To find the value of x in the given equation, we can use the transposition method. The transposition method involves moving the terms containing x to one side of the equation and the constant terms to the other side.

Let's solve the given equation step by step:

Step 1: Distribute the fractions on both sides of the equation:
(x-4)/2 - (x-3)/2 = 1/6

Simplifying the equation, we get:
(x-4 - x+3)/2 = 1/6

Step 2: Combine like terms:
(-4 + 3)/2 = 1/6

Simplifying further, we get:
-1/2 = 1/6

Step 3: Multiply both sides of the equation by the common denominator, which is 6, to eliminate the fractions:
6 * (-1/2) = 6 * (1/6)

This gives us:
-3 = 1

Step 4: Since -3 is not equal to 1, the equation has no solution.

Conclusion:
After solving the equation using the transposition method, we found that the equation has no solution. Therefore, there is no value of x that satisfies the given equation.