QUESTION: How can I know the tithi of a particular day?

Just measure the arc between the sun and moon at sunrise of that day, divide that by 12, and round up.

This is a sunrise (see the Sun conjoined Asc?).

The Moon is a little more than trine to the Sun. Trine is 240°. It is about 4° past that, so it is at about 244° at the time of Sunrise at this place (Japan)

244 divided by 12 is 20 1/3. Round that up to 21. It is the 21st Tithi on this day, at this place.

What is “the 21st tithi”? 15 is the full moon, the 16th is the 1st of waning. So the 21st is 6th waning tithi (Ṣaṣti, Kṛṣṇapakṣa).

Calendar software will confirm it.

You may notice it says Sunrise was 5:07, but the chart I showed was for 5:12. This is because the Sun is huge. It covers an entire half a degree. So it technically rises a little before the exact conjunction. It seems that about 1.5° prior to conjunction is the visual sunrise.

The calendar software i showed is available here.