The rate of the reaction is determined by the rate law, which is typically expressed as Rate = k[A]^m[B]^n, where m and n are the orders of the reactants. If k = 3, A = 2 M, and B = 2 M, and the reaction is kA^2B, then the rate would be 3 x (2)^2 x (2) = 24 M/s.
A + 2 B ==>C + Drate = k[A][B]^2 if this is an elementary step. If not, you cannot determine rate equation.So, #1 would be the best answer, i.e. rate = kAB2 but the square only applies to B and not to A, so it isn't really written correctly.
The rate constant must have units that make the rate equation balanced. For example, if the rate law is rate kA2B, the rate constant k must have units of M-2 s-1. To calculate the rate constant, you can use experimental data and the rate law equation to solve for k.