OK. this is what I understand:
The question was about 2/4 signature. There is NO double four time thing in signatures.
Duple four time -yes, there is such a thing and I will try to explain it.
duple (not double) = in music means two beats to the bar ( or what\'s between the two sets of parallel bars).
If he wants to know what\'s 2/4 that\'s \"two in four time\" = it\'s two beats in each bar and a quarter note gets the beat.
IF you say duple four time it\'s 4/2 and that reads as four beats in each bar and half note gets one beat. HOWEVER, you do not read that as double four time. There is no such thing.