[lrhyner]

I am really not understanding the concept behind this question. I thought Br would be the leaving group, but I know the structure should form an alkene

[discodermolide]

I think the two different alkenes are shown in the drawing.
The H and Br require to grand and anti-periplanar for the elimination to succeed well. This configuration is reached in the reaction giving molecule J.
This condition is reached in molecule K by using one of the hydrogens of the methyl group.