Your Bhagyank is every digit of your date of birth added together and reduced to a single digit. For 14 November 1988 that is 1 plus 4 plus 1 plus 1 plus 1 plus 9 plus 8 plus 8, which is 33, and 33 reduces to 6. Unlike the Mulank it uses the whole date, so it changes with the month and the year as well as the day.
Write the date out in digits, add every digit, and reduce the total to one digit. The Bhagyank makes no intermediate reductions: the day, month and year are not reduced separately before being added, which is exactly what the Life Path method does.
The two therefore differ whenever an intermediate 11, 22 or 33 would have survived one route and not the other. This page reports the all-digits result, the Life Path page reports the reduce-then-add result, and both show the working, so you can see precisely where a difference comes from instead of guessing which site is wrong.
Ank Jyotish as practised today pairs the two: the Mulank from the day alone, the Bhagyank from the full date. Because the Mulank has only nine possible values and the Bhagyank nine more, most people carry a pair rather than a single number, and practitioners look at whether the pair is harmonious.
AstroZivi computes that comparison but is explicit about what it rests on. The number-friendship grid behind any harmonious or clashing verdict has no located source, classical or modern, and it is not the planetary friendship scheme of Brihat Parashara Hora Shastra ch. 3, which disagrees with it for several numbers. It is shown as common practice, labelled as such.
Each of the nine Bhagyanks is assigned a ruling planet: 1 Sun, 2 Moon, 3 Jupiter, 4 Rahu, 5 Mercury, 6 Venus, 7 Ketu, 8 Saturn, 9 Mars. The tool prints your number with its planet and, where the total was a master number before the final reduction, notes that too.
The table matches Cheiro's Book of Numbers of 1926, and that is the furthest back this app can trace it honestly. Mulank and Bhagyank are living Indian usage with no located Sanskrit locus, so the site names the modern work rather than inventing a chapter and verse to make the row look as authoritative as a classical one.
For educational purposes. Astrological interpretations are traditional and not a substitute for professional advice.