Count Unique instances across several Columns

I have a spreadsheet with several columns (20 odd) and several thousand rows (10187!)
See "data" Tab for a watered down version
I need to count the total number of shifts worked (for a given period - say monthly)

Ie: in the data sheet Equip # 111 - how many shifts did it work in April , then May

There are several line descriptions for each date & shift worked
Some work day & night shift - some only work days

I would like a formula - Not sorting/filtering -( I can do that) but I am doing this all the time & would like a better more robust way to calculate.

Thanks if you can help.
Leigh