We are given the expression:

$\log_3 18 - \log_3 8 + \log_3 4$

To simplify this expression, we will apply the logarithmic properties:

1. Logarithm subtraction: $\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right)$
2. Logarithm addition: $\log_b A + \log_b B = \log_b (A \times B)$

Step 1: Apply the subtraction property.

$\log_3 18 - \log_3 8 = \log_3 \left(\frac{18}{8}\right) = \log_3 \left(\frac{9}{4}\right)$

Step 2: Apply the addition property.

$\log_3 \left(\frac{9}{4}\right) + \log_3 4 = \log_3 \left(\frac{9}{4} \times 4\right)$

Simplifying: $\log_3 \left(\frac{9}{4} \times 4\right) = \log_3 9$

Step 3: Simplify the result.

$\log_3 9 = 2$

Therefore, the simplified result is: $\boxed{2}$

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. How do you apply logarithmic properties to expressions with different bases?
2. Can you solve $\log_3(54) - \log_3(6)$?
3. What is the logarithmic form of $3^x = 27$?
4. How do you simplify $\log_b (A^n)$ using logarithmic rules?
5. What is the value of $\log_5 25 + \log_5 5$?

Tip: When working with logarithms, always look for ways to use properties like product, quotient, or power rules to simplify complex expressions.