How many parallelograms are there in the following figure?

The given figure is a grid of parallelograms consisting of 2 rows and 4 columns.
To form a parallelogram, we need to choose 2 horizontal parallel lines out of the total available, and 2 slanted parallel lines out of the total available.

* Total number of horizontal lines = $3$
* Number of ways to choose 2 horizontal lines = $\left(\genfrac{}{}{0ex}{}{3}{2}\right)=\frac{3\times 2}{2\times 1}=3$
* Total number of slanted lines = $5$
* Number of ways to choose 2 slanted lines = $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=\frac{5\times 4}{2\times 1}=10$

Total number of parallelograms = $\left(\genfrac{}{}{0ex}{}{3}{2}\right)\times \left(\genfrac{}{}{0ex}{}{5}{2}\right)=3\times 10=30$.