, 2020

Solution:

Note that since there are 8 faces to a regular hexagonal prism and a cross-section may only intersect a face once, the upper bound for our answer is 8.

Indeed, we can construct a cross-section of the prism with 8 sides. Let $A B C D E F$ and $A' B' C' D' E' F'$ be the two bases of the prism, with $A$ being directly over $A'$. Choose points $P$ and $Q$ on line segments $A B$ and $B C$, respectively, and choose points $P'$ and $Q'$ on segments $D' E'$ and $E' F'$, respectively, such that $P Q \parallel P' Q'$. Then, the cross-section of the prism from the plane that goes through $P, Q, P', Q'$ forms a polygon with 8 sides.