  In this paper we use min-max theory to study the existence free boundary
minimal hypersurfaces (FBMHs) in compact manifolds with boundary $(M^{n+1},
\partial M, g)$, where $2\leq n\leq 6$. Under the assumption that $g$ is a
local maximizer of the width of $M$ in its comformal class, and all embedded
FBMHs in $M$ are properly embedded, we show the existence of a sequence of
properly embedded equidistributed FBMHs. This work extends the result of
Ambrozio-Montezuma [2].
