Let's solve the expression step by step:

Given expression:

$3 \left[\frac{(8 - 4)^5}{8}\right]$

1. Subtract inside the parentheses:

$8 - 4 = 4$

So the expression becomes:

$3 \left[\frac{4^5}{8}\right]$

2. Calculate $4^5$:

$4^5 = 1024$

Now the expression is:

$3 \left[\frac{1024}{8}\right]$

3. Divide $1024$ by $8$:

$\frac{1024}{8} = 128$

4. Multiply by 3:

$3 \times 128 = 384$

So, the final answer is:

$\boxed{384}$

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How would the result change if the exponent was 4 instead of 5?
2. What if the expression inside the parentheses was $(8 + 4)$ instead of $(8 - 4)$?
3. Can you solve $2\left[\frac{(7-2)^3}{5}\right]$?
4. How does the value change if the 3 outside the brackets is replaced by 5?
5. How do you simplify the expression if there are variables involved, like $3\left[\frac{(x - 4)^5}{8}\right]$?

Tip: Always remember to perform operations inside parentheses first, followed by exponents, before moving on to division, multiplication, addition, and subtraction (PEMDAS/BODMAS).