Countifs criteria difficulty

I'm trying to count the number of units installed and removed between two dates, along with narrowing it down to a specific machine and product type created with the units. The installation date and removal date are both logged into separate columns within a different sheet. The hope is to make something similar to a search feature in that the criteria can be changed and the formula will update results rather than using filters on the original data sheet. Where am I going wrong?

=COUNTIFS({Machine #}, =[3]@row, {Product Type}, =[2]@row, ({Date Installed}, >= ([4]2), {Date Removed}, <= ([5]2)))