The given expression is:

$6\left(\dfrac{1}{2}w - \dfrac{3}{4}\right)$

Let's simplify this step by step:

1. Distribute the 6 to both terms inside the parentheses:

$6 \times \dfrac{1}{2}w - 6 \times \dfrac{3}{4}$

2. Simplify each term:

• $6 \times \dfrac{1}{2}w = 3w$
• $6 \times \dfrac{3}{4} = \dfrac{18}{4} = 4.5$

3. Therefore, the simplified expression is:

$3w - 4.5$

Let me know if you want more details on the steps or have any questions!

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Here are five related questions you could explore:

1. How would you simplify $5\left(\dfrac{2}{3}x + \dfrac{1}{6}\right)$?
2. What happens if you add 4 to both sides of the equation $3w - 4.5 = 0$?
3. How would you solve $3w - 4.5 = 12$ for $w$?
4. What is the result of simplifying $8\left(\dfrac{3}{4}x - 1\right)$?
5. How would you factor the expression $3w - 4.5$?

Tip: When distributing a constant over a fraction, multiply the constant by the numerator and then divide by the denominator for easier calculations.