Let's simplify the given expression step by step:

\(

\frac{(81^{\frac{3}{4}} - 27^{\frac{1}{3}})}{3 \times 2^3}

\)

First, let's evaluate the exponents:

\(

81^{\frac{3}{4}} = (3^4)^{\frac{3}{4}} = 3^{4 \cdot \frac{3}{4}} = 3^3 = 27

\)

\(

27^{\frac{1}{3}} = 3^{\frac{3}{3}} = 3^1 = 3

\)

Now we can substitute these values back into the expression:

\(

\frac{(27 - 3)}{3 \times 2^3}

\)

Simplify the numerator:

\(

\frac{24}{3 \times 2^3}

\)

Simplify the denominator:

\(

\frac{24}{24}

\)

Finally, cancel out the common factor:

\(

1

\)

Therefore, the value of the given expression is \(1\).