How would I go about solving the following problem? There were different questions with matrices in them, but this one was different from the others.

For the matrix product

[ -5 , 3 ][ 6 , -3 ]
p = [ 2 , -2 ][ 4 , -3 ],

determine the expression that gives the value of p12.

I tried multiplying the matrix and got

[ -18 , 6 ]
[ 4 , 0 ].

I wasn't sure where to go from here.

Your product matrix is correct.

p12 is the element in row 1, column 2: 6

Looks like you need to review the introductory material on matrix notation!