How to count the number of checked Checkboxes with Rules?
Yes this is perfectly possible with Rules, and you don't need any PHP to get the job done. In your case, the crucial part of such rule is a Rules Action to perform a Loop. If you're not familiar with such loops, then I strongly recommend to have a look at the tutorial titled "Lists and loops".

In your case, you should use (at least) these Rules Actions:


"Add a variable" (say with a machine name like nr_of_checked_terms), with initial value "0".
Add a loop related to your taxonomy terms. After you do, you should iterate over each item in that list (= each taxonomy term). And for each iteration you should then perform a Rules Action to "Set a data value", whereas you actually increment the value of nr_of_checked_terms with "1".


After the loop finished, the value of nr_of_checked_terms will be the actual number of terms that were checked. Just add another Rules Action near the end to do your actual multiplication using nr_of_checked_terms as one of the available tokens.

Done

PS 1: Refer to my answer to "How to set multiple values to an unlimited Term Refence field with Rules" for some sample rules that are like a variation of your question here.

PS 2: I assume this is about D7 ...