How to solve 2/3(b-6)

2/3(b-6)
is an expression with the variable b.
We can simplify the expression using the distributive properties of multiplication:
(2/3)(b-6)
= (2/3)b - (2/3)6
= (2/3)b - 4

If the expression was meant to be an equation, it would have been written with an equality sign, such as
2/3(b-6) = 0
In this case, we simplify the expression on the left hand side:
(2/3)b -4 = 0
Add four to each side to isolate the variable:
(2/3)b = 4
Multiply each side by (3/2) to transform the coefficient of b to 1
(3/2)(2/3)b = 4*(3/2)
b = 6
is the answer sought.

MathMate - the distributive properties of multiplication is what I was attempting to use ... however, i am trying to get a clearer picture of how how you derived the answer (2/3)b - 4? Please explain

The distributive property of multiplication over addition/subtraction can be summarized by the following identities:
a(b+c) = ab + ac
a(b-c) = ab - ac
For example:
5(4+3) = 5*4 + 5*3 (both add up to 35)
5(4-3) = 5*4 - 5*3 (both evaluate to 5)
If we apply the second identity, distribution over subtraction, to the given expression,
(2/3)(b-6)
we get
(2/3)(b-6)
= (2/3)b - (2/3)6 ... and simplify
= (2/3)b - 2*6/3
= (2/3)b - 4

got it - thank you

Great!