Hello!
The answer is:
Anna will need 27 posts.
Why?
To calculate how many post does she need to place at the corners and every 2 feet around, we need to calculate the perimeter of the garden plot.
So, we can calculate the perimeter of the garden plot (rectangle) using the following formula:

We know that:

Then, calculating the perimeter of the garden plot, we have:


Now, calculating how many post she will need, we have:

Hence, we have that Anna will need 27 posts.