Why people more frequently say "三四个", less frequently say "三五个" or "四五个" or "五六个", and even more less frequently say "四六个"？
1. About 三四个，四五个，五六个 and ballpark numbers
It's common to express ballpark quantities with adjacent numbers.
三四个 means about three or four. Same works for 四五个，五六个.
Thus you can infer the use and meaning of 一两个，两三个，六七个，七八个，etc.
Example: 鸡汤里放多少个八角？五六个就够了。
It's less common to use such expression for numbers bigger than ten, but you certainly can!
For number bigger than ten: 十一二个 or 十一十二个，十二三个，十三四个，etc.
Example: 聚会来了几个人？大概十五六个人吧。
The reason it's less common for numbers bigger than ten, is likely because people would prefer to ballpark it on the scale of tens, it's also less awkward-sounding.
To further explain, imagine about 27-30 people came to my party. If I try to say 大概二十七八个人吧。It's long and awkward-sounding, it's also confusing to just read it! Thus, people would just say 将近三十人吧。(Almost thirty people.)
2. About why 三五个 is more frequently used
I will explain my best guess. First of all, 三五 is a kind of a special combination just by itself, it's used in classical Chinese literature to describe date, days, age, decades, it's also used in expressions related to astronomy, fengshui. The only reason I could come up with why 三五个 is widely accepted is because of the idiom/chengyu 三五成群。It means a small group of people.
Example: 这辈子我就三五个挚友。
3. About why 四六个 is not an expression
As I explained earlier, Chinese use adjacent numbers to express ballpark. 四 and 六 are not adjacent. You can infer the same for 五七个，七九个，etc.
If you look closely at google search results, you would find out 四六个 is NOT used by itself. It's often separated by punctuation, like: “主题四：六个实战案例”，“四-六个月大的宝宝”，or used as part of a sentence “二四六个字押韵的诗词”.