Let's analyze the given expression and simplify it step by step:

The expression is: $2\sqrt{54} - \sqrt{18}$

Step 1: Simplify the square roots

Simplifying $\sqrt{54}$:

$\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}$ Thus: $2\sqrt{54} = 2 \times 3\sqrt{6} = 6\sqrt{6}$

Simplifying $\sqrt{18}$:

$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$

Step 2: Substitute the simplified forms

Now substitute these simplified forms into the original expression: $2\sqrt{54} - \sqrt{18} = 6\sqrt{6} - 3\sqrt{2}$

Step 3: Match with the provided options

From the given choices, the expression $6\sqrt{6} - 3\sqrt{2}$ matches Option C.

Thus, the correct answer is C: $6\sqrt{6} - 3\sqrt{2}$.

Would you like a further breakdown of any part of the solution?

Here are some related questions to deepen your understanding:

1. How do you simplify radical expressions?
2. What are the properties of square roots when simplifying?
3. Can square roots be added or subtracted directly?
4. How do coefficients affect square roots in expressions?
5. What is the difference between exact values and approximate decimal values of square roots?

Tip: When simplifying radicals, always look for perfect squares within the number under the square root.