Thank you all!
“texi” and “thi” are combinations that work.
Joel, I mentioned the site, because I think this is site specific setting. I practice at my workplace sometimes, and it doesn’t have any IME (let alone Japanese) installed. Sites like RealKana, iKnow, ReadTheKanji and such don’t require Japanese IME to work, only the correct letter combination. What they think is “correct combination”, that is XD