Vapnik-Chervonenkis Dimension: why cannot four points on a line be shattered by rectangles?
The definition of "a set $P$ can be shattered by rectangles" is that for every subset of $P$, there is a rectangle that contains precisely that subset and excludes the rest of $P$. Equivalently, every labeling of the points as positive and negative is consistent with at least one hypothesis in $H$.

Now consider four points $p,q,r,s$ along a line in the plane.  Since there is no rectangle that contains $p$ and $r$ but excludes $q$ and $s$, these four points cannot be shattered by rectangles.