How do you get grass to grow on a small area that is constantly walked on? The ground has become packed down and hard.
You need to loosen the soil. Shovel or pitchfork. Mix in peat moss and compost into it.
The soil needs to be softened. You can soak it with water (the easy way) so it is mud and spread the seed and put straw over it, OR you can till a shallow amount and rake it (more work) then add water every day once the moisture is about gone. Grass thrives in cooler and wetter climate. ACTUALLY, I wait until fall to do this because the weeds die back and allow the grass to get a good hold. You want it at the end of summer so there is lots of time to grow before cold weather. Feed it when it gets up a couple inches and let it grow to a height that makes it bend over some before cutting it.
If that area is constantly being walked on, the ground will compact again over time. Have you thought about putting some kind of easy walkway on that path? Here's some ideas: