Proportional segments between parallelogram and triangle In the figure, ABCD is a parallelogram, $F$ is in the prolongation of $AD$. If $EF=32$, $GF=24$ and $AD=DF$, $BE=?$ I made the drawing![enter image description...--prophetes.ai

Proportional segments between parallelogram and triangle In the figure, ABCD is a parallelogram, $F$ is in the prolongation of $AD$. If $EF=32$, $GF=24$ and $AD=DF$, $BE=?$ I made the drawing![enter image description here]( _My try:_ I tried to do some proportions between the triangles $FDG$ and $BCG$ but got nothing. I'm 100% sure that this problem is about propotionality. Any hints?

By intercept theorem, $BG=GF=24$

$BE=BG+GF-EF=24+24-32=16$