I have my own docker private registry created in my host machine[localhost] and I intend to make use of localhost private registry to pull images in google Kubernetes engine.
How do I make it happen?
You won't be able to use either your locally built docker images (which can be listed by running docker images on your local machine) or your locally set up docker private registry (unless you make it available under some public IP which doesn't make much sense if it's your home computer). Those images can be used by your local kubernetes cluster but not by GKE.
In GKE we generally use GCR (Google Container Registry) for storing images that are used by our Kubernetes Engine. We can build them directly from code (e.g. pulled from our github account) on a cloudshell vm (simply click Cloud Shell icon in your GCP Console). You can build them directly on this machine and you can push them to your GCR directly from there.
Alternatively, if you build your images locally, but by "locally" I mean this time the nodes where kubernetes is installed (so in case of GKE they need to be present on every worker node), you can also use them without a need of pulling them from any external registry. The only requirement is that they are available on all kubernetes worker nodes. You can force kubernetes to always use your local images, present on your nodes, instead of trying to pull them from a registry by specifying:
imagePullPolicy: Neverin your Pod or Deployment specification. More details on that you can find in this answer.