［Solution］Since there are only 4 types of rule lines: horizontal, vertical, left diagonal, and right diagonal, there are at most 4 rule lines passing through each point. Therefore, there are at most 24 rule lines passing through 6 given points. However, in this counting process, each line is counted at least twice, so there are at most 12 different rule lines. If there are exactly 12 rule lines, then there are exactly 4 lines passing through each point, and exactly two given points on each rule line.

Consider the convex polygon $M$ formed by the 6 given points. Clearly, each rule line passing through two given points passes through the interior or an edge of $M$. In this way, the internal angle at each vertex of $M$ is not less than $135^{\circ}$. On the other hand, the sum of the interior angles of a convex hexagon is $720^{\circ}$, the sum of the interior angles of a convex pentagon is $540^{\circ}$, the sum of the interior angles of a convex quadrilateral is $360^{\circ}$, and the sum of the interior angles of a triangle is $180^{\circ}$. In any of these cases, the smallest internal angle is less than $135^{\circ}$, which is a contradiction. Therefore, among the lines connecting the six points, there are at most 11 rule lines.

The figure on the right shows that 11 rule lines are connected between the 6 points, so the maximum number of rule lines that can be connected between 6 points is 11.
7.17 Lines in the plane that are parallel to the $x$-axis, $y$-axis, or the bisectors of the quadrants are called regular lines. Among all the lines connecting 6 points in the plane, what is the maximum number of regular lines?