How to calculate Vapnik-Chervonenkis dimension

I think you just need to think carefully about how your examples relate to the definition. The VC dimension of H is the maximum h such that there exists a set of cardinality h shattered by H. To show that VC(H)=4 you must show:

• There is a set of cardinality 4 shattered by H, and
• Any set of cardinality greater than 4 is not shattered by H

In the picture, they are doing the first thing - giving a lower bound on the VC dimension by giving an example of a set that is shattered. To show VC(H)<5 they should also show that no set of five points is shattered.

There will in general be lots of sets of various sizes that are not shattered, but that doesn't matter, essentially because VC dimension is a maximum over sets that are shattered. Your example of $n$ points on a line does not imply anything about the VC dimension. I hope this helps.