What is period given by y=-2sin (2pi/7x)

Whenever the things contained by the sin function = a factor of 2pi, a complete cycle is made.

so in this case, whenever 2pi/7x = 2pi, a complete cycle is made.

2pi/7x = 2pi

1/7x = 2pi/2pi

1/7x = 1

7x = 1

x = 1/7

therefore, the period is x = 1/7 for every cycle