The speed equation for simple harmoic motion is given by; omega x the square root of the amplitude squared - the displacement squared.
Omega can be calculated because omega = 2pi x frequency, which because f = 1 / T, can be written as omega = 2pi / T.
Also, we have to change units to metres, therefore 10 cm and 6 cm become 0.10 metres and 0.06 metres, respectively.
Plugging these back into the speed equation, we are left with, speed = (2pi / 0.8) x the square root of (0.10)^2 - (0.06)^2, which will give you 0.6283185307 ms-1.
Rounding this off, we are left with 0.6 ms-1, which is A.