There are apparently 30723072 ways to draw this flower. But why?

This picture was in my friend’s math book:

Below the picture it says:

There are 3072 ways to draw this flower, starting from the center of
the petals, without lifting the pen.

I know it’s based on combinatorics, but I don’t know how to show that there are actually 3072 ways to do this. I’d be glad if someone showed how to show that there are exactly 3072 ways to draw this flower, starting from the center of the petals, without lifting the pen (assuming that 3072 is the correct amount).

Answer

First you have to draw the petals. There are 4!=24 ways to choose the order of the petals and 24=16 ways to choose the direction you go around each petal. Then you go down the stem to the leaves. There are 2!22=8 ways to draw the leaves. Finally you draw the lower stem. 24168=3072

Attribution
Source : Link , Question Author : user265554 , Answer Author : Ross Millikan

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