What is the number of segments in the picture i have no Idea how i can do this. I guess it is 8*8 = 64, but that isn't the right answer:
What is the number of segments in the picture below? Each segment joins two circles.

 A: Look at the middle line of points formed by the intersections of the line segments. Count how many segments run through each point, counting the left- and rightmost points as having one segment intersecting them. 

Each consecutive point will have one more segment intersecting it than the last until you get to the middle; then the number works its way back down. You will notice that if you count this way, you will not count any segment more than once, since a segment cannot intersect more than one point.

 $$1+2+3+4+5+6+7+7+6+5+4+3+2+1 = 56$$

As you might have guessed, this is equivalent to

 $$\begin{align} & (7+1)+(6+2)+(5+3)+(4+4)+(3+5)+(2+6)+(1+7) \\ &= 8+8+8+8+8+8+8 \\ &= 8\cdot 7 \\ &= (\text{# top circles})\times(\text{# bottom circles})\end{align}$$

A: Since all of the nodes are connected, each node at the top “shoots out” a single segment for each node at the bottom, and each node at the bottom “receives” a single from each node at the top. Since a “received” segment is the same as a “shot out” segment, just count the segments as originating from the top row.
Each top node shoots out $7$ segments (one for each bottom node) and there are $8$ top nodes. Thus there are $7\times8=56$ segments. We did not double count because none of the segments touch more than one top node.
This logic is reversible, so the bottom nodes could be considered the “originators,” so long as you realize that if you count all of the segments touching one row of nodes, you don’t count the segments touching the opposite row, because they are all the same segments.
A: Your graph is $K_{8,7}$, a complete bipartite graph, making all links between two groups of vertices (the "parts") but no links between vertices in the same part. There are $7$ nodes in the part at the top of the diagram and $8$ nodes in the part at the bottom of the diagram.
To check that it is complete, you can just count the degree of each of the $7$ vertices at the top of the diagram - they are all degree $8$,  so there are $56$ edges. 
A: $8$ bottom nodes, each with $7$ segments $= 56$.
$7$ top nodes, each with $8$ segments $= 56$.
Since every segment is double counted, we need to divide the total by two: $\dfrac{1}{2} (56+56)= 56$.
A: Each circle on the top is connected to each circle on the bottom. So to pick a segment we need to pick one circle on the top and one circle on the bottom. There are 7 circles on the top and 8 circles on the bottom. So by the rule of product, the number of segments is 7 times 8 =56
