We can read and discuss this paper

https://www.frontiersin.org/articles/10.3389/fpsyg.2020.00038/full

@Sanjeev @Irfan has suggested a very well articulated publication to your cause. However, you can refer to below article as well.

https://www.frontiersin.org/articles/10.3389/fpsyg.2019.00799/full

Hello Sanjeev Kumar. You wrote:

I have 4 variables say W XYZ, x is directly related to y, and w moderates the relationship between x and y , and this w is further moderated by z.

You appear to be describing the following model:

Y = b0 + b1X + b2W + b3Z + b4XW + b5XZ + b6WZ + b7XWZ + error

The null hypothesis for the 3-way interaction states that nature (or "size") of the two-way interactions does not depend on the level (or value) of the 3rd variable. E.g., you are interested in the X*W interaction. The null hypothesis for the 3-way interaction states that the nature of the X*W interaction does not depend on the value (or level) of Z. If the 3-way interaction is statistically significant, you conclude that the nature of the X*W interaction does depend on the value of Z. And that, I assume, is what you mean when you talk about moderated-moderation.*

* Personally, I have never been a fan of using the word moderation as a synonym for interaction. Originally, authors like Cohen et al. talked about moderation and augmentation as two forms of interaction effects--see the attached image. I'm not entirely sure when it happened, but at some point people started using moderation as a more general term that subsumes both forms. I think that effect moderation works much better as a general term for interaction, as it does not commit to the form of the interaction (moderating vs augmenting). YMMV.

Dear Sanjeev Kumar,

The usual answer will be as you said: H1: x will explain y, moderated by w. However, in the second part, the answer will be "depend". Depend on how it will moderate the variable. Hayes has different models and could help you describe it, if you have 2 moderators in 2-way interactions or a 2-way and 3-way interactions.

Here you can have more information:

Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford Press.

I hope I could help you.

Dear Sanjeev Kumar though it looks "fancy" to say moderated-moderation and, as Amalia Raquel Pérez Nebra mentioned, Hayes has provided unbelievable types of moderating effects in his books on PROCESS, it is literally impossible to theoretically defend this type of unusual moderation models. Other than paid platforms, where getting through the gate is relatively easy even in very high impact journals, you will very rare find published work on such models. If you still insist to opt for moderation of the moderation, try to find theoretical foundation and justification for the one first. Writing a hypotheses or analysis are small issues in this case. Tq.

It depends on how it will moderate the variable. Hayes has different models and could help you describe it, if you have 2 moderators in 2-way interactions or a 2-way and 3-way interactions.