This is quite difficult to try to explain so I'm going to set up some matrices to demonstrate as best as I can. If matrix A has 3 rows and 2 columns, it would be respresented as [tex] A_{3*2} [/tex]. This matrix can only be multiplied by another matrix that has the same number off rows as the number of columns in A. For example, if matrix B has 2 rows and 3 columns, it would be represented as [tex] B_{2*3} [/tex]. If we set them next to each other, it might be easier to see the rule: [tex] A_{3*2} B_{2*3} [/tex]. The 2's match, and the other numbers represent how your solution matrix will look. Your solution matrix will be a 3x3. Here is matrix A: [tex] \left[\begin{array}{ccc}1&2\\3&4\\5&6\end{array}\right] [/tex] and here's B: [tex] \left[\begin{array}{ccc}1&2&3\\4&5&6\\\end{array}\right] [/tex]. We can multiply these according to the rules. The multiplication works like this: [tex] \left[\begin{array}{ccc}1&2\\3&4\\5&6\end{array}\right] * \left[\begin{array}{ccc}1&2&3\\4&5&6\\\end{array}\right] [/tex]. first row of A times first column of B: (1*1)+(2*4) = 9. that goes into row 1 column 1 of your solution matrix. Go va to row 1 in A but column 2 in B: (1*2)+(2*5) = 12. That goes into row 1 column 2 of your solution matrix. Next row 1 of A and column 3 of B: (1*3)+(2*6) = 15. That goes into the first row column 3 of the solutiong matrix. Now move to row 2 of A column 1 of B: (3*1)+(4*4) = 19. That goes into row 2 column 1 in your solution matrix. Next row 2 A, column 2 B: (3*2)+(4*5) = 26. That goes into row 2 column 2 solution matrix. Continue as I showed you. You should be fine.
