To write the statement "I think of a number, multiply it by 3, subtract 6, and multiply the result by 4" algebraically using $x$ as the unknown:

1. Represent the number as $x$.
2. Multiply it by 3: $3x$.
3. Subtract 6: $3x - 6$.
4. Multiply the result by 4: $4(3x - 6)$.

The algebraic expression is: $4(3x - 6)$

Would you like a detailed explanation of the steps or further assistance? Here are some related questions to deepen understanding:

1. How would this expression change if the subtraction were performed after multiplying by 4?
2. Can you expand $4(3x - 6)$ to simplify it further?
3. What happens if you divide the entire expression by 2? What does it represent?
4. How can you use this algebraic expression to solve for $x$ if a specific result is given?
5. Can this process be represented using function notation?

Tip: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) when constructing or solving algebraic expressions!