Ignore the solution they have provided and think on your own
In the final reaction you need 2B2O3 on the right so, you need to flip A so and multiply by 2. This gives 2B2O3 on the right.
After flipping A you get 2B2H6 on the left which is not there in the final reaction. So, you need to multiply B by 2 so that the B2H6 can cancel out.
In flipping A we get 3H2O(g) on the right. So, flip D and multiply by 3 to cancel out the H2O(g). Now in flipping D we get 3H2O(l) on the right so to cancel it flip C and multiply by 3.
Now if you add everything you should get the required reaction.
Now you should be able to understand what has been done in the solutions