Let's form all the possible strings that end in two Ds.
First put the two Ds at the end --> _ _ _ D D
There's 1 way to do that.
We have 3 more places but we have the complication of the Es which are repeated.
Let's count them separately, based on the number of Es.
If there are 0 Es, then we have 4 letters left.
4 choices for the first blank
3 choices for the second blank
2 choices for the third blank
4 * 3 * 2 = 24 ways
If there is 1 E, it can go in 3C1 = 3 places leaving two blanks
4 choices for the first remaining blank
3 choices for the second remaining blank
3 * 4 * 3 = 36 ways
If there are 2 Es, they can go in 3C2 = 3 places leaving one blank.
4 choices for the remaining letter to put in that blank
4 * 3 = 12 ways
If there are 3 Es, they go in all the empty spots in 3C3 = 1 way leaving no more blanks
Adding those up we have:
24 + 36 + 12 + 1
= 73 ways
P.S. It's always good etiquette to go back and award a Best Answer. It's about the only way that you can recognize someone that volunteered their time to help you. As a side benefit, you get 3 points back to ask future questions, so it is a win-win. If you don't go back, you'll get a reputation as someone that just asks without returning the favor and people will be less likely to help you on future questions. Think of it as a virtual thank-you; I'm assuming your parents taught you it was always polite to say thank-you, right? :)