Unfortunately the OP seems to have forgotten about her question in this forum, although I sent her a PM and she logged in today: Last access to course Wednesday, 16 January 2019, 10:41 PM (17 hours 41 mins)
Joseph Rézeau
Posts made by Joseph Rézeau
"if for example, they picked the word 'Cat' and matched it with the picture of the frog, then it would mark it as incorrect."
OK, because the word "cat" and the image of a frog do not match.
But why would you not accept it if the student matched the word "cat" with the image of the cat? Because the cat is not an amphibian?
I maintain that the way your question is formulated is totally misleading for the student. This is not so much a matter of finding the right type of question as one of re-formulating your question so that it is clear to the student what you want them to answer.
Marcus rightly points to the Gapfill question type. That would work, but without the images. See below:

Another possibility is to use the H5P plugin with its Drag & Drop activity, as illustrated below:

I'm afraid your drag & drop question does not make sense for the end-user (student). From your display it is obvious that the student will want to drag each label to the matching picture, without taking account of your instructions.
I suggest you clarify your pedagogic objectives in asking your question in such a confusing (to the end-user) way.
Your question is not specific to the Quiz activity, it's a general course format question.
You might try the Flexible sections format plugin.

@Zeid,
If you are not familiar with the github procedures it's not easy to explain in a few words. Since your fixes are really minimal, only a few lines of code (and you have attached the files to your previous message), I expect that will be enough for the plugin maintainer, Mike, to fix things up when he reads this discussion and when he has the time to do it.