The trick is that for "admit" we use exactly the same verb as for "to thank"!
To thank is להודות (from "thank you - תודה) and to admit is... להודות!
The change lies in... of course, as expected - in the preposition!

When saying that we are thankful to somebody we, quite logically, use the LE- preposition, and if being thankful about - על.

Here are some examples:
⮞ הוא מודה לנו על העזרה (audio #1)
He thanks us for the help
⮞ איך לא חשבת להודות להם על מה שהם עשו לנו בעבר?! (audio #2)
How come you haven't thought of thanking them for what they did for us in the past!
⮞ תודה לאל, הוא בריא ושלם! (audio #3)
Thank G-d, he is safe and sound!

But when we use another preposition, BE-, then it changes the meaning of the verb completely, turning it into "admit"!

See some examples:
⮞ הפושע מסרב להודות במה שעשה (audio #4)
The criminal refuses to admit what he did.
⮞ הגיע הזמן להודות בכל המעשים הרעים שעשית! (audio #5)
The time has come to admit all the bad things you did!
⮞ תודה באמת - אתה לא מסוגל לקחת ארחיות (audio #6)
Admit the truth - you are incapable of taking responsibility!

Unfortunately, the preposition is not always necessary... and sometimes this verb is left without any preposition - and then the meaning has to be guessed!
But it's not that hard - we have our best fried with us - the context! I'm never tired of saying that Hebrew is very context dependent, with all our vowel-less writing, context is often the ultimate key to understanding!

Here are two more more examples - is it difficult to guess which is which? :)
(translation at the very bottom)
⮞ אני חייב להודות, לא הספקתי להגיש את מסמכים בזמן, אבל אני מוכן לפצות על זה! (audio #7)
⮞ להודות וללמוד לקבל היא הדרך הכי טובה להרגיש מאושר (audio #8)