Looking at the picture, there are 4 phases.

- Draw the petals
- Draw the upper stem
- Draw the leaves
- Draw the lower stem

Lets label these $A,B,C,D$. Clearly, the total number of ways to draw the flower is simply;

$$Total = A \times B \times C \times D$$

We can see that the upper and lower stem are un-ambiguous; i.e. there is only one way to draw them. Thus $B=D=1$. So our equation becomes

$$Total = A \times C$$

Now lets look at the leaves first. The factors in it are:

a. Which leaf do you draw first?

b. What direction do you use for the first leaf?

c. What direction do you use for the second leaf?

There are 2 possibilities for each, so $C=2\times 2 \times 2=8$.

Now lets look at the petals.

a. Which petal do you draw first? (4 choices)

b. Which petal do you draw second? (3 choices)

c. Which petal do you draw third? (2 choices)

d. Which direction do you draw the X petal? (2 choices for each petal)

So $A=4 \times 3 \times 2 \times 1 \times 2^4=24 \times 16=384$.

And

$$Total=A \times C = 384 \times 8 = 3072$$