To get a 2 from the combined process, you either need a 1 first time (prob. 1/6) and then a 2 (prob. again 1/6); or you get a 2 first time (prob. 1/6) and then another 2 (prob. 1/5 this time, because there are only the five numbers 2,3,...,6 to choose from). So the probability of the combined process returning a 2 is .
Continuing in that way, the probability for each of the remaining numbers being returned by the combined process is:
prob. that it is 3 is ,
prob. that it is 4 is ,
prob. that it is 5 is ,
prob. that it is 6 is .
As a check, you can add the six probabilities and see that their sum comes to 1.