Alternative approach: count carbons. N-methylpiperidine's ring has five carbon atoms; none are destroyed, so the final hydrocarbon must have five carbons, ruling out 1,3-butadiene (four) and ethene (two). Two rounds of Hofmann elimination are needed; each pushes its new double bond toward the end nearest where nitrogen last was attached. This gives double bonds at 1-2 and 4-5, i.e. penta-1,4-diene.
\[\boxed{\text{Penta-1,4-diene}}\]