Not can addition be confusing but so can multiplication; multiplication is another one of the those things that we do because we were told to. multiplication can also be confusing in different base just like in addition.
one way to do multiplication in a different base or just general multiplication is to create pictures. You can think of multiplication as an array of number or a rectangle. Below are two pictures of the rectangle method.
The rectangle method is easy to understand, but when we switch base it can be confusing. We can use the cookie method to help with multiplication of different bases. The pictures below show multiplication of base 5 and base 6.
We can also use other methods besides the rectangle and the cookie method. We can use the Statndard Multiplaction (pictured below).
Or we can use the Partial Products (pictured below).
In Partial Products we can see why we carry and how we arrive at an answer to the problem.