Before we subtract, we need to make sure we're working with two of the same type of numbers.
What do I mean by this? Imagine if you have two groups of things - for this example, we'll say those things are bananas. If you add a set of 2 bananas and a set of 3 bananas, you'll end up with a set of
2 bananas + 3 bananas = 5 bananas
But if we're adding two things of different types - say, 2 bananas and 3 apples - we'll need to make sure to give the result the correct name; 2 bananas + 3 apples ≠ 5 banapples, but 2 bananas + 3 apples does = 5 fruits.
Ninths and thirds are both things in the same way that apples and bananas are, but they're a very precise type of thing. One ninth (1/9) is the size of one part when we split one whole into 9 equal parts, and one third (1/3) is the size of a part when we split one whole into 3 equal parts (I've included an illustration of this at the end).
To subtract two thirds (2/3) from seven ninths (7/9), we'll need to convert one of them so that their denominators (their names (or types)) match. Notice that, in order to go from splitting a whole into 3 equal parts to splitting it into 9 equal parts, we need to triple the number of parts, or multiply it by 3. That means that, for every 1/3, we're creating 3/9. If 1/3 triples to 3/9, it would make sense that 2/3 triples to 6/9.
Now that we've turned our thirds into ninths, we're ready to subtract:
7/9 - 6/9 = 1/9
So, our result here is 1/9.