Did the new tour guide remember to stop in the Ancient Greek gallery?
Sometimes, it is helpful to rearrange sentences into additional forms in order to understand them more fully. The sentence you have been given is in the interrogative form, meaning that it is a question. You could rearrange it into a declarative sentence (a statement) by writing, "The new tour guide remembered to stop in the Ancient Greek gallery." By looking at both these versions of the sentence, we can identify more clearly how it is constructed.
Remember that the "subject" of a sentence is simply what a sentence is about. If we write a very simple sentence, such as, "The dog ate the bone", it is easy to understand that the subject is ABOUT the dog and the dog's action. In other words, the dog is the one taking the action; the bone is the thing which is being acted upon.
Now look at your original sentence in this same fashion. What is the sentence really ABOUT? Is it about the new tour guide, or about the gallery? The easiest way to answer to decide what is taking the action. In this case, is the gallery, itself, taking action? No, only the new tour guide is taking the action. We know this by identifying the "action words" (verb phrase). The action is "remembering to stop"; the Ancient Greek gallery is simply the place involved in making the stop. The action is done by the new tour guide. Therefore, the SUBJECT is "the new tour guide".
Which of the words in this phrase is the most important one? Is it "new", "tour", or "guide"? Try leaving out each of the four words, to see if the sentence still makes sense. If we left out the first word, "the", the sentence could still be understood, even though it would be bad English.
We could also leave out the words, "new" and "tour", because they only add description. However, if we left out the word "guide", as in "Did the new tour....remember to stop at the Ancient Greek Gallery," we obviously cannot know what the sentence means. Therefore, we absolutely cannot understand the sentence without using the word "guide".
Now that we have identified the word "guide" as being absolutely essential to understanding the sentence, and that the guide is the one taking the action, we know that "guide" is the subject of the sentence. We can also tell that the word "new" merely tells us WHICH tour guide, and the word "tour" only tells us what type guide. So, these words are only descriptive of the guide, himself or herself.
The only word in the subject which is absolutely essential is the word "guide". Therefore, it is the "simple subject". If we at the words "the", "new", and "tour", we are describing the guide. This, then, is the "complete subject".
I hope this helps you understand how to identify simple and complete subjects.