Iterating through a column and counting criteria that is met if that row meets a condition

Hello,

I have a large range of cells that each have a list associated with them, such as Bag, Box, Cart, Tray. Another column in the range of cells has months associated with the rows. My goal to count how many of each option there is for a given month and doing so over a range of cells. I have found similar ideas using BYROW() and COUNTIF(). COUNTIF() works as expected, but I can't get the BYROW() to work how I want. Attached is an example of what I am trying to do with an equation that I tried and failed at.


Thanks for the help.