Indicate the model that meets the conditions II.1, II.2, II.3 and not II.4. In this case, you need to indicate a set of points and a ternary relation in this set.
Ordering axioms:
II1. If B lies between A, C, then A, B, C are different and lie on one straight line.
II2. If A, B, C are different points on a straight line and B is between A, C, then B is between C, A.
II3. If A and C are two points on a straight line, then there is at least one point B lying between A and C and at least one point D lying such that C lies between A and D.
II4. Of any three different points on the straight line, there is always one and only one which lies between the other two.
Consider the standard Euclidean plane $\mathbb{R}^2$ with relation:
$$B \text{ lies between } A \text{ and } C :\iff \left(A\neq C \text{ and } B \text{ is the midpoint of segment } AC\right)$$
Btw, it's not a question about Hilbert spaces.