When do you use "che" and when "di" for comparisons?
Why is "I intend to know" incorrect?
Is it better to say "Penso di sapere" or "Penso che so" for this translation?
"Penso di sapere" is better.
"Penso che so" is wrong.
Another possibility would be using the subjunctive "Penso che io sappia meglio l'inglese del francese" but subjunctive is pretty difficult, better going for the easiest solution. :)
Why is "I think that I know" wrong?
actually, I had it wrong because I didn't put what you said, which, in formal tests such as the TOEFL it would be wrong, being the "that" unnecessary.