Our ancestors' counting style was "Ippon, nihon, san bon, shi hon" until about 150 years ago. (Please try to listen Katsura-Beicho's Koten Rakugo). The reason why Shi had changed into Yon was probably military needs. (It's hard to distinguish Ni and Shi in battlefield). So that counting style also had changed but "hon"of "shi hon" was remained. 三本是自然生的说法。四本是人工的说法。原来是不一样的。

Linguistically it is called 'sequential voicing,' which is 'rendaku' in Japanese. There are a number of theories to generalize the rules, but none of them is really successful:/ It would be better to simply memorize it. I am sorry. I know my answer does not really help you, but there are not many irregular forms, so you can do it:)

Thanks Ryoko! XD

I agree with Shogo-san's answer if your question is for the pronunciations of 本. It happenes with other numbers: ippon, nihon, sanbon, yonhon, gohon, roppon, nanahon, happon, kyuuhon, juppon... Besides, it also happens with other counters which begin with はひふへほ like 分 杯 匹 etc.