Two combined automation tools that the administrator can use to create the task record and assign based on date criteria are:
Create a formula field to capture the MAX date. A formula field is a custom field that calculates a value based on other fields or expressions. In this case, a formula field can be used to capture the maximum value between Estimated Shipping Date and Client Need By Date fields and store it as a date value.
Make a Process Builder to create the task. A Process Builder is an automation tool that allows you to create processes that perform actions based on certain criteria. In this case, a Process Builder can be used to create a task record when a certain condition is met and assign its due date based on the formula field value.
The other two options are incorrect because:
An approval process is an automation tool that allows you to route records for approval based on certain criteria and approval steps. It does not create or assign tasks based on date criteria.
A workflow rule is an automation tool that allows you to perform actions based on certain criteria and evaluation time. It does not create or assign tasks based on date criteria.