When a die is rolled there are six possible outcomes. If the die is rolled twice, there are thirty-six ( 6 x 6 = 36 ) possible outcomes.
(1) If the sum of the two rolls of the die is six, and the number 4 occurred on one of the rolls, then there were two possible ways that could have happened; a four on the first roll and a two on the second roll, or a two on the first roll and then a four on the second roll. So the probability is 2/36 or 1/18.
(2) exactly similar to (1), there are two ways that this could happen so the probability again is 1/18.