What is the process to find the product of 6x107 for 5th grade

Line it up vertically ...

107

6

... then multiply 7 by 6, and carry the 4:

107

6

2

Then multiply the 0 by 6 and add the carried 4 to the product of the 0 and 6:

107

6

42

Then multiply 1 by 6:

107

6

642