Let's express the given information in equations:

"a is multiplied by 3" can be represented as 3a.
"the result is 4 less than 6 times b" can be represented as 6b - 4.
From the given information, we can set up the equation:

3a = 6b - 4
Now, let's solve for a:
3a = 6b - 4
Divide both sides of the equation by 3:
a = (6b - 4) / 3

Next, let's find the value of a - 2b:
a - 2b = [(6b - 4) / 3] - 2b
We can simplify this expression by finding a common denominator:
a - 2b = [(6b - 4) - 6b] / 3
Simplifying further:
a - 2b = (-4) / 3
Therefore, the value of a - 2b is -4/3.
So, the correct answer is B. -4/3.