Four lines join the apex of a large triangle to its base, and two more lines cross it parallel to the base.

Explanation

1. 01

   From the top vertex there are 6 lines in all: the two sides and the 4 inner lines. Any 2 of them form a triangle with a horizontal line as the third side.

2. 02

   Pairs of lines from the vertex: $\binom{6}{2} = 15$.

3. 03

   Horizontal lines that can close them: 3 (the base and 2 parallel lines).

4. 04

   Triangles $= 15 \times 3 = 45$.