It doesn't matter why you rolled a die or how many sides that die has: if you roll a 2, a 4, or a 6, the corresponding ability will trigger.

If you roll more than one die at a time, Dee Kay's abilities will trigger for each corresponding result. For example, if I roll 2, 2, and 4 on three six-sided dice, her second ability will trigger twice and her third ability will trigger once.

If you roll a 2, a 4, or a 6 while rolling to visit your attractions, and one or more visit abilities also trigger from that roll, you choose the order in which those abilities and Dee Kay's ability go on the stack. You can have Dee Kay's ability resolve before those visit abilities, after them, or in between any of them.

If the spell or ability that caused you to roll a die includes any effects due to the result, resolve those effects before putting Dee Kay's triggered abilities on the stack.