We can simplify the expression $\log_3{18} - \log_3{8} + \log_3{4}$ using logarithmic properties.

Step 1: Apply the logarithmic subtraction rule

The subtraction of two logarithms with the same base can be written as the logarithm of a quotient: $\log_3{18} - \log_3{8} = \log_3\left(\frac{18}{8}\right) = \log_3\left(\frac{9}{4}\right)$

Step 2: Apply the logarithmic addition rule

The addition of two logarithms with the same base can be written as the logarithm of a product: $\log_3\left(\frac{9}{4}\right) + \log_3{4} = \log_3\left(\frac{9}{4} \times 4\right) = \log_3{9}$

Step 3: Simplify the logarithm

Since $9 = 3^2$, we can simplify $\log_3{9}$: $\log_3{9} = \log_3{(3^2)} = 2$

Thus, the value of the expression $\log_3{18} - \log_3{8} + \log_3{4}$ is $\boxed{2}$.

Do you want more details on any step, or have any questions?

Here are some related questions:

1. How do the properties of logarithms work for division and multiplication?
2. How do you simplify logarithmic expressions with different bases?
3. What are the key logarithmic identities used in complex expressions?
4. Can you solve an equation with logarithms like $\log_3{x} = 2$?
5. How does changing the base of a logarithm affect its value?

Tip: Remember, when simplifying logarithmic expressions, always check if the numbers can be written as powers of the base to simplify the calculation further.