To solve this expression, we can use the properties of logarithms.

First, let's simplify each individual logarithm using the power rule:
log(23)2/3 = log(23)(2^(1/3)) = (1/3)log(23)2
log(23)6 = log(23)(6) = log(23)2 + log(23)3
log(23)4 = log(23)(4) = log(23)2^2 = 2log(23)2

Now, we can substitute these values in the original expression:
(1/3)log(23)2 + log(23)3 - 2log(23)2
= (1/3)(1) + log(23)3 - 2(1)
= 1/3 + log(23)3 - 2
= 1/3 + log(23)3 - 2
≈ 1/3 + 1.5563 - 2
≈ 0.3333 + 1.5563 - 2
≈ 0.3333 + 1.5563 - 2
≈ 1.8896

Therefore, the value of the expression log(23)2/3 + log(23)6 - log(23)4 is approximately 1.8896.