This is the 377th most frequent Hungarian word.
tudom
"I know."
In this sentence, 'tudom' means 'I know', referring to possessing knowledge about where the book is.
Én tudom, hogy hol van a könyv.
I know where the book is.
Here, 'tudom' expresses the possession of knowledge, in this case, the lack of it about solving the problem.
Még nem tudom, hogyan oldjam meg ezt a problémát.
I do not know yet how to solve this problem.
The verb 'tudom' here represents that the speaker has known something for a significant period of time.