The problem asks to evaluate the expression:

$\log_2 4 + \log_2 12 - \log_2 6$

Let's solve this step-by-step using logarithmic properties:

1. Simplify each logarithmic term:

   • $\log_2 4 = \log_2 (2^2) = 2$.
   • $\log_2 12 = \log_2 (4 \times 3) = \log_2 4 + \log_2 3 = 2 + \log_2 3$.
   • $\log_2 6 = \log_2 (2 \times 3) = \log_2 2 + \log_2 3 = 1 + \log_2 3$.

2. Substitute the simplified values into the expression:

   $(2) + (2 + \log_2 3) - (1 + \log_2 3)$

3. Simplify the expression:

   $2 + 2 + \log_2 3 - 1 - \log_2 3 = 4 - 1 = 3.$

Therefore, the value of the expression is:

$\boxed{3}$

Would you like more details or have any questions?

Related Questions:

1. How do you simplify logarithmic expressions involving products and quotients?
2. What are the properties of logarithms used in solving this problem?
3. How can we change the base of a logarithm to make calculations easier?
4. How do logarithmic scales work, and where are they applied in real life?
5. What is the relationship between exponential and logarithmic functions?

Tip: Always remember that $\log_a (xy) = \log_a x + \log_a y$ and $\log_a \left(\frac{x}{y}\right) = \log_a x - \log_a y$.