Countif with same criteria in multiple columns

So I've got a spreadsheet for my football team which shows stats for the players over the season. I've recently started noting what positions people play, and I want to be able to filter the stats by the position. The challenge is that some people play multiple positions over the course of a match, so I've ended up with several columns for the position played.

The below picture is some test data which I've simplified. As you can see, if I put "Primary" and "LB, it correctly pulls 6 matches for Alex and 0 for Tim. What I want is to be able to put "Any" and "LM" and it to return the 3 matches which Alex played at LM. I found a previous thread where Sum and Mmult were used but I couldn't figure out how to get something like that to work with my data. I've attached the original sheet for reference.
sample.PNG