How does nan change counter's kana?

彼は何____が。。。(ひき)
hiki becomes biki. Is there a chart or something to know when the kana will change like this?

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It is called 連濁 (れんだく). This article is a fair introduction.

Only kana which are unvoiced and can become voiced (i.e., kana which can take 濁点 (だくてん・the little voicing marks like は taking ば) can transform like this, clearly. The actual patterns of how and when they will change or not entirely consistent but in general it is restricted to native Japanese words. It is much easier to pick up than it probably initially seems. There are some exceptions or even the choice to use/not use it with some words (e.g., 三階) but in most cases one is correct and the other is incorrect. There is also some minor variation between some dialects but you probably won’t notice this for a while.

The reason it exists is because “it is easier to say”. In the case of なん or 3 (さん) the final sound is ん which, if you pronounce it correctly, is closer to the English M than N in these kind of cases (I am on dangerous ground here but just for the sake of illustration take this to be true). Try saying nambiki vs namhiki and you may see how it is “easier to say”.

Good luck and happy studies!

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Thank you!

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There is a chart in the back of the genki textbook that I used all the time.