Separate the 12 face cards from the rest of the deck. Assume that the remaining cards have been shuffled. Select THREE cards from the face cards.

Question: Select a card from the remaining deck. DO NOT replace the card. Select another card. What is the probability that a red 3 is selected and a face card is selected?

I'm having a rough time understanding you completely. We separate the face cards from the deck and select 3 from those 12 face cards which are separated. Correct.

Now, we have 40 non-face cards left and we select two cards from it. Correct?

If we choose 2 cards from the 40, we can not get a face card because they have been separated. Or are we mixing the three face cards we selected from the face card pile into the deck of 40 non-face cards and then making our selections? Just want to clarify before I try to explain. Don't want to do the wrong thing.

I wrote it wrong. Sorry

Out of a 52 card deck remove the red cards from the deck and assume that the remaining cards have been shuffled. Select a card from the remaining deck. Do Not replace the card. Select another card. What is the probability that a red 3 is selected and a face card is selected?

Do you want the probablilty of both happening or the probablity of getting a red 3 on the first pick and then the probability of getting a face card on the second pick?