Hi,

For this you might have to create a new form in the website for entering the task details and record it. You can create a custom form similar to the contact us form by code or you can use the form builder module for the same. 

Modules:

1. HTML Form Builder

2. Website Form Builder

If you are an enterprise user, the custom module is not necessary as this option is available by default in enterprise version.

If the form is creating from the code, refer the contact us form in the website.

Thanks