For Matrix Multiplication, you have to sure the matrix sizes are compatible. This means when the dimensions (rows x columns) are put side by side, the inner numbers match. The new matrix takes the size of the outer numbers.
For BD, B has dimensions (2 x 2) and D has dimensions (2 x 1)
The inner numbers are (2 x 2) and (2 x 1) which means the matrix multiplication will work.
The size of the product matrix will be the outer numbers, (2 x 2) x (2 x 1) = (2 x 1).
Good luck with the rest :)