To understand the answer you should know the answer for this question1
Question 1: Given an n length string how many ways it can be splitted.
ab/cd/e a/bcd/e ab/cd/e.....so on
Try to answer this question and then read below solution.
Given a recursive language We can construct turing machine for L* like this
step 1: split the input W in all possible ways. (Using TM we can do it) the no of ways is solution to the question1
step 2: for each split w1#w2#w3...simulate TM of L on all the strings w1,w2,w3... and if it accepts all the strings w1,w2,w3 then Accept W.
Here you are accepting the string if it is concatenation of some strings which are all members of L.