class.cs

public class ClassA
{
    private readonly ClassB _classB;
    private readonly ClassC _classC;

    public ClassA(ClassB classB, ClassC classC)
    {
        _classB = classB;
        _classC = classC;
    }

    public async Task<int> DoWork()
    {
        var taskC = _classC.NotThreadSafe("test");
        var taskB = _classB.DoWork();

        await Task.WhenAll(taskB, taskC);

        return await taskC;
    }
}

public class ClassB
{
    private readonly ClassC _classC;

    public ClassB(ClassC classC)
    {
        _classC = classC;
    }

    public async Task<int> DoWork()
    {
        return await _classC.NotThreadSafe("");
    }
}