I suspect what's throwing you is your identification of the longest linear chain, the "parent alkane chain." In the examples in class, it always works out that the longest linear chain happens to be the horizontal one... but it doesn't have to be. I think you're numbering left to right and assuming that the horizontal carbon chain must be the parent alkane. In which case, it absolutely does look like a propyl group is coming off of carbon 6. The key here is that the longest linear chain does not have to be horizontal. The longest linear chain starts at the left, goes to carbon 6, then kinks and continues to carbon 9.
If you were assume the propyl group is the substituent, then your parent chain would only be 7 carbon atoms long, and you would name it 5-ethyl-2-methyl-6-propylheptane. but if you kink the parent chain, then it becomes 9 carbon atoms long. Then the substituent at carbon 6 is the methyl group and you end up with the name 5-ethyl-2,6-dimethylnonane.
see the image for the two ways of naming the molecule. This is a common 'gotcha' question professors love. The longest linear chain does not have to be horizontal, and you should not assume it always will be.