Function invocation every second time
Code style is not the problem. The expectation is that a new coder uses the in house style guides when writing.

I think the problem is that you missed an important assumption. 

The test case passes one argument, however that does not mean that the function you are given will have only one argument.

Thus maybe (I am just guessing) if you wrote... 

const alternate = fn =&gt; {
    let odd = false;
    return (...args) =&gt; (odd = !odd) ? fn(...args) : undefined;
};


Also though not stated there could have been an expectation that it not throw on bad input. Thus first vet the input function.

const alternate = fn =&gt; {
    let odd = false;
    return typeof fn === "function" ?
        (...args) =&gt; odd = !odd ? fn(...args) : undefined :
        () =&gt; {};
}


or

function alternate (fn) {
    if (typeof fn === "function") {
        let odd = false;
        return (...args) =&gt; odd = !odd ? fn(...args) : undefined;
    }
    return () =&gt; {};
}


As the documentation does not say anything about throwing an error the safer bet is to silently deal with bad input