rate = k * [A]^2 * [B]^1
Use the data from any trial to calculate k.
k = (rate)/([A]^2 * [B]^1)
E.g., for Trial 1, we have
rate = 3.0×10−3 M/s
[A] = 0.50 M
[B] = 0.010 M
Plug those numbers in and crank out the answer.
Now with the calculated value of k, calculate the initial rate for [A] = 0.50 M and [B] = 0.075 M
rate = k * [A]^2 * [B]^1
k = calculated value
[A] = 0.50 M
[B] = 0.075 M