You really don't need any help on the question. It's all right there in the picture. What you need help with is the answer.
The number of times the same thing happens each second is called its "frequency". The frequency of the dragonfly's flaps is 477 Hz. (If you're close enough to the dragonfly, you can hear the wings flapping. It sounds like a raspy tone with a frequency of 477 Hz.)
The "period" is just the length of time it takes to happen once. That length of time is just (1 / frequency) .
The dragonfly flaps its wings once every (1 / 477 Hz) = 0.0021 second (C)