'anything' in that case, has more impact than 'everything'.

"The dog can eat anything." is like saying, "There is nothing the dog can't eat." Which is a lot more emphasis than just saying, "The dog can eat everything."

Hope this helps..!

" "A world,where anything is possible" .."a world ,where everything is possible...whats the difference?"

are they synonymous in this case??? ...is there an element of "emphasis" that would make them different in the same context? For instance, if I used anything, does is it stronger than using everything?

Another example:

You can do/get everything you want vs. You can do/get anything you want