We have been having a lot of success at our house with Partial Product Method. You just put the answer to each part of the multiplication problem down in total under the line, putting space markers for the number of numbers behind the numbers you are working on. For the example above, for the first part of the problem, 6x5= 30, instead of putting the 0 under the line and the 3 at the top of the next column, you just put the full 30 under the line. Then you go on to the next part, 6x3=18 and first count how many numbers are behind, or to the right of the number you are working on and you see that there is only one (the 5) so you put one line to mark that place value. Then you put the full 18 down after the place-holding mark. You continue on with the problem, putting the full answers down under the line, with the appropriate place-holding lines. Then you add all of the numbers below the line and you get your answer. I discovered this method on the Five J's blog and Joy has a wonderful video explaining the method step by step.
I think it is particularly good for kids with dyscalculia or other learning disabilities, but it is also great for regular learners. It simply is an easier method. It is wonderful for the teacher as well, because it is so easy to find out what went wrong if a student gets a wrong answer. You can quickly tell if it is a multiplication mistake, a place value mistake or an addition mistake.