一个both by和by both的问题，求指点！！！！！！！！

维以不永伤6

从manhattangmat forum上面看到的，转问一下：unlike the commercial crafts of many other countries, those of thailand are influenced by both ancient beliefs and tradition and have remained relatively unchanged over the years.

what is the difference in this sentence if the term both by is used instead of by both?

and is there a difference btwn the two terms if the sentence stopped after "tradition" (taking away the last "and ..." part)？
求指点！！！谢谢。。。