There really is no trick at work here. You just need to find all the triangles you can.
Look carefully so you don't miss any triangles that are hard to spot.
Several triangles can share a single side.
To make matters even more confusing, you need to look at every side of the big triangle to find all the triangles. Make sure you don't accidentally count a single triangle twice during your search.
US Version
First, go ahead and count the large triangle all by itself. Then, add one of the three lines that splits the big triangle into two. Now your total has grown to three triangles.
Next, add one more line to your big triangle and you'll create three new triangles. There are three combinations of two lines possible.
Good luck finding the rest.
UK Version
Imagine that the only line on the diagram is the one extending downwards from the topmost point of the triangle. It divides the large triangle into two smaller triangles. That makes three triangles so far.
Now add the other two lines back into the diagram one by one and count how many more triangles are made. Be careful not to count the same triangle twice.
Solution
Incorrect
Give it another shot!
Spotting triangles may seem easy, but there are quite a few to find here. Look carefully.
Correct
Great job!
You can see the complete list of triangles above. For such a simple picture, that's a lot of triangles!