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Solution

The figure is a $2 \times 4$ grid of small parallelograms. To find the total number of parallelograms, we can choose any two of the $2 + 1 = 3$ slanted "rows" and any two of the $4 + 1 = 5$ slanted "columns". So, the total number is: $ \displaystyle \binom{3}{2} \times \binom{5}{2} = 3 \times 10 = 30 $