Explanation:

To solve the problem, let's consider the expansion of terms:

- The expression is $[1+2/x{]}^9[1-2/x{]}^9$.

- Notice that this can be rewritten as $[(1+2/x)(1-2/x){]}^9$.

- Simplifying inside the brackets, we have $(1+2/x)(1-2/x)=1-(2/x{)}^2$.

- This becomes $(1-4/x^2{)}^9$.

Now, expand using the binomial theorem:

- A general term in the expansion $(1-4/x^2{)}^9$ is given by $(\genfrac{}{}{0ex}{}{9}{k})(-4{)}^k(x^{-2k})$.

- Each term depends only on $k$, ranging from 0 to 9.

- Therefore, there are a total of 10 distinct terms in the expansion.

Correct option: Option 2 - 10