Six different ways, for small word problems like this, you can just write it out like (A,B,C), (A,C,B), (B,C,A), (B,A,C), (C,A,B), and (C,B,A) where A=Alice, B=Ben, and C=Carlos
The perimeter is the sides of the hexagon. One of the hexagon edges is shared with a rectangular face. Solve for that edge. 78/6=13. The height is the length and edge is the width. Area is length(16) times width(13). 16•13=208. The answer is 208mm^2