In To Kill a Mockingbird, what does Mr. Nathan Radley know about the intruders in his garden ?

The incident with Mr. Nathan Radley comes about in Chapter 6 of To Kill a Mockingbird.

When Dill airily suggests that they take a walk, Jem is eager, but Scout is indignant about the boys' true reasons for doing so, which is to peek into one of the loose shutters at the Radley home. The boys want to see if they can catch a glimpse of Boo Radley without drawing attention to themselves, hence the secret night 'mission.'

As it turns out, the trio manage to get into the back yard of the Radley lot. Jem and Scout help Dill up to the window which has a hanging shutter; unfortunately, Dill sees nothing from this vantage point but a light in a distant room. The boys resolve to try a back window instead, while Scout worriedly warns the boys against such a foolhardy action. In the meantime, Scout spies what she thinks is a shadow of a man moving towards Jem's direction. Fortunately for Jem, the shadow stops just beyond him, turns and then walks back to where it came from.

Relieved at the reprieve, Jem hurriedly ushers both Dill and Scout through the collard patch. However, Scout trips noisily on some collards, and the booming sound of a gunshot rings through the night in response. Frightened beyond comprehension, the children rush for the fence which abuts the school yard. They return home safely, but Jem has lost his pants in the struggle at the school fence.

The children spy some neighbors gathering by the Radley place and glimpse Mr. Nathan Radley standing inside his gate with a shotgun on his arm. Atticus, Miss Stephanie, Miss Maudie, Miss Rachel, and Mr. Avery are there as well, but no one sees the children come up.

Eventually, Miss Maudie notices the children and asks whether they heard all the commotion. According to Miss Maudie, Mr. Nathan Radley has 'shot a Negro in his collard patch.' Miss Stephanie comments next, and her words provide some indication of Mr. Nathan Radley's thoughts on the intruders in his collard patch that night:

“No,” said Miss Stephanie. “Shot in the air. Scared him pale, though. Says if anybody sees a white nigger around, that’s the one. Says he’s got the other barrel waitin‘ for the next sound he hears in that patch, an’ next time he won’t aim high, be it dog, nigger, or—Jem Finch!”

Despite the lack of any empirical evidence to support his claim, Mr. Nathan Radley adamantly proclaims that the intruders were black. He assumes that the intruders meant to steal from his collard patch. Furthermore, his racist assumptions are echoed by both Miss Maudie and Miss Stephanie. So, from Mr. Nathan Radley's point of view, the intruders were black and meant to steal from his collard patch; this is what he believes he knows.