Count elements in a collection based on a condition [Java 8]
The code looks very nice! However, here my small complaints:
Tests
The tests are good, but you're testing the Behaviours implicitly, when you test the Counter. The Counter itself does only the following things: stream, filter with the given predicate, and count. The static methods im Behaviours should be tested separately, as should the logic of the Counter. The problem is, if the test fails, you don't know if the problem is the Counter or the Behaviours. The more &quot;implicit&quot; things you test, the harder is it to find the bug.
You're testing with too many values. The logic itself should be the same with two values (one is a palindrome, one is not) as with four values (two palindromes, two not). If the behaviour for two or four values is different, then it's two different test cases.
The lists to count/filter can have a better name.
To make a test case more readable, it's usually split in the three blocks given/when/then, separated by an empty line. Setup the test data / perform the action / assertion.
Also, I recommend, but that's personal preference, to static import static methods, at least the assertion methods, so it looks a bit more clean.
What's missing (at least what I couldn't find):

You're missing the test for even numbers.
You're missing the test for 0/1 number in testCountingPrimeNumbers.
What happens for an empty String (or string with length 1 or 2) in the palindrome count?

Other

check-prefix: The convention is to use a is prefix, if a method returns a boolean, it's more clear than &quot;check&quot;.
test-prefix in test methods: That was the convention for JUnit3 (I think), when annotations weren't a thing. It's not needed anymore, when you use the @Test annotation, so instead of testCountingPrimeNumbers, you can go with countPrimeNumbers.
The JavaDocs for the test methods are obsolete, the method names are clear.
I'd get rid of the System.outs, too, you get enough information in the junit test report.
Instead of naming stuff actual, I'd give it the proper name, e.g. amountOfPalindromes. And maybe not declare the expected variable.

Hope this helps...