We can label the figure as shown.
The simplest parallelograms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHKL.
These are 6 in number.
The parallelograms composed of two components each, are ACGE, BDHF, EGKI, FHLJ, ABJI and CDLK.
Thus, there are 7 such parallelograms.
The parallelograms composed of three components each, are ADHE and EHLI. i.e. 2 in number.
The parallelograms composed of four components each, are ACKI and BDLJ. i.e. 2 in number.
There is only one parallelograms composed of six components, namely, ADLI.
Thus there are 6 + 7 + 2 +2 + 1 = 18 parallelograms in the figure.
Hence, total number of parallelograms are 18
