How do you know when to use que/qui instead of ce que/qui

Question

Accepted Answer

Bonjour Helena, That's a very interesting question indeed! Let's point out first that we're talking about the relative pronouns here, which are used to introduce a new information in a sentence (as opposed to question words like "what?").  Once you know this, the separation is quite simple: "qui/que" can mean "who/which/that ..." whereas "ce qui/ce que" mean "what ...".
La fille que je regarde. (The girl whom[m]/that I'm watching.)Je fais ce que je veux. (I do what I want.)
I hope that's helpful!

Answer

Precision: in cases where "ce qui / ce que" would also be translated by "which" in English, you need to ask yourself: What does "que/qui/ce que/ce qui" is referring to? If it refers to a noun (expressed before), then you will use "que/qui". If it refers to the whole part of the sentence, the whole idea, then it will be "ce que/ce qui". 
Les gens que je rencontre ... (The people which I meet...)-> Here "que" refers to "people"
J'aime les bananes, ce que tu trouves fascinant. (I love bananas, which you find fascinating.)-> Here "ce que" refers to the whole fact that I love bananas, not just to the bananas
 :)

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Bonjour Ron !
In the case you pointed out, I agree that if what was found fascinating was only the bananas, you could use que, as follows :
J'aime les bananes que tu trouves fascinantes.ATTENTION, as it would mean something slightly different here:I love the bananas that you find fascinating.
Bonne journée !

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Thank you!!! That was so clearly explained too - even if I'm confused in the future I now know how to figure out which one to use! :)

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J'aime les bananes, ce que tu trouves fascinant. (I love bananas, which you find fascinating.)
Here "ce que" refers to the whole fact that I love bananas, not just to the bananas. . .
While I understand the explanation given, using the rule of thumb about following a noun, "If it refers to a noun (expressed before), then you will use "que/qui"."  then que could also be correct, i.e. he finds bananas fascinating -- of course in reality that would be interesting that someone found bananas fascinating, like he/she had never seen a banana.
I do believe the better example is:  "Je fais ce que je veux. (I do what I want.)"

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And this confusion is exactly why I don't get this lesson... still... after weeks of trying it just won't go in.  The whole "introducing new information" idea above just makes no sense to me at all... :-(