Calculate the rate of the Pacific Plate's motion in cm per year for the island sequence Kauai to Oahu. Can you show me the steps. Note that...

I assume that the data in your assumes it would take 2.1 x 10^6 years for the Pacific Plate to move the 181 km distance from Kauai to Oahu.  If so, then:

1 km = 100,000 cm = 10^5 cm

181 km = 18,100,000 cm = 1.81 x 10^7 cm

1.81 x 10^7 cm / 2.1 x 10^6 years = .8619 x 10^1

which rounds up to 8.62 cm / year.