To start you would turn 4 2/3 into a mixed number by multiplying 4 and 3 and adding 2. Your mixed number would be 14/3. Then, you want to find how many 2/3 yard long pieces of string will fit into 14/3 so you devid 14/3 by 2/3 and you get 7. So 7 2/3 yard pieces of string will fit into 4 2/3.
To check your work you can multiply 2/3 by 7 and you will get 4 2/3.