The time constant is calculated using the following rule:
T = RC
where:
R is the value of the resistance = 600 ohm
C is the value of the capacitor = 0.01 * 10^-6 Farrad
Substitute with the givens ti get the time constant as follows:
T = 600 * 0.01 * 10^-6
T = 6 * 10^-6 seconds = 6 microseconds