By lowest terms, it simply means to it's simplest form. To do that, you have to find a number that can divide the two numbers involved. That number is 2. When 2 divides 18, you get 9. When 2 divides 32, you get 16. So you get;
9/16. And that is the final answer because nothing else can divide the two numbers. To make you understand better, i am using a different fraction. So;
16/8
Once again, 2 can divide. But you can also use 8. If you use 2, it will be 8/4, 2 can still divide, so that will be 4/2. 2 divides again, making it 2/1, which is the same as 2.
If you use 8, it will be 2/1. Which is still 2. So as you can see, no matter the number used, the answer remains the same. Hope i helped. Have a nice day.