What is p(4,4) on two consecutive rolls of a number cube

The probability of rolling 1 number, a four, on a 6-sided number cube, is 1/6.
On the second roll, the probability of rolling 1 number, a four, is again 1/6 (remember theoretical probability for one event does not consider previous rolls).
But the probability of rolling a four on 2 on consecutive rolls will be the probability of the first event times the probability of the second event. Think of it as rolling a four on the first time and the second time, and whenever there is "and" you need to multiply the probabilities. The probability of rolling a four on two consecutive rolls is 
(1/6)*(1/6) = 1/36.