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Pooja NekkalapudiPooja Nekkalapudi 

Page redirect from roweventhandle to the home page

case 'logacall': this[NavigationMixin.Navigate]
({ type: 'standard__objectPage',
attributes: { objectApiName: 'task', actionName: 'new' },
state : { defaultFieldValues:"WhatId=" + this.Id} });
break;

How to navigate to the Homepage after that save of new task, right now this takes to the new task record
 
AshwiniAshwini (Salesforce Developers) 
Hi Pooja,
To navigate to the homepage after saving a new task record , you can use the NavigationMixin with the standard__home page reference type.
You can refer below sample code:
import { NavigationMixin } from 'lightning/navigation';

// ...

 navigateToHomePage() {
        this[NavigationMixin.Navigate]({
            type: 'standard__namedPage',
            attributes: {
                pageName: 'home'
            },
        });
    }
Related:https://salesforce.stackexchange.com/questions/393248/how-to-navigate-user-to-home-page-after-logging-in-lwr-site-in-lwc 
https://www.sfdcpoint.com/salesforce/navigation-service-in-lwc/

Thanks