A triangle has two lines from its top vertex to the base and one line across it, parallel to the base.

Explanation

1. 01

   From the top vertex there are 4 lines in all: the two sides and the 2 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: $\binom{4}{2} = 6$.

3. 03

   Horizontal lines that can close them: 2 (the base and 1 parallel line).

4. 04

   Triangles $= 6 \times 2 = 12$.