How to create a generic extension method?

The first error is because Length is a property of the String class while in your generic version the type of the T parameter is not known. It could be any type.

The second error is because you return just the query object but not the actual result. You might need to call ToArray() before returning.

With little modifications you could come up with this:

public static class ExtensionOperation
{
    public static IEnumerable<T> AlphaLengthWise<T, L>(
        this IEnumerable<T> names, Func<T, L> lengthProvider)
    {
        return names
            .OrderBy(a => lengthProvider(a))
            .ThenBy(a => a);
    }
}

Which you could use like this:

string[] names = { "Jon", "Marc", "Joel", "Thomas", "Copsey", "Konrad", "Andrew", "Brian", "Bill" };
var result = names.AlphaLengthWise(a => a.Length);