Both of these are equally correct:
I don't think this can be the the right answer.
I don't think this could be the right answer.
The word could is the past-tense and conditional-mood form of can. Consequently, could has a softer, less-confident or less-forceful shade of meaning in situations where both words make sense.
Here are a few examples to illustrate:
"No one can fool me" sounds a little more certain than "No one could fool me."
"You can wash the dishes" is a stronger hint than "You could wash the dishes."
"I can save $200 a month" is more confident than "I could save $200 a month."
"Can you save $200 a month?" asks for a simple check of your current income and expenses. "Could you save $200 a month?" asks you to exercise ingenuity or make extra effort, if necessary, to find a way to save that much.
"Can you meet me at 8:00?" is a more forceful request than "Could you meet me at 8:00?" You would say "Can you…?" to a good friend, with whom you feel comfortable omitting niceties of politeness.
These are subtle differences in shades of meaning, which can't be reduced to rules. It's probably better to pick them up through experience communicating with the language than by memorizing descriptions of them. The more you use could in situations of the form "If we had X, we could do Y", the more it starts to feel softer than can, even in situations where there is no "if" or stated condition.