Is it possible to add variables (fields) /some matter like "hi ,this request needs supervisors approval" in the task ?
Discussion posts and replies are publicly visible
The screenshot you've posted is from the auto-generated task notification email Appian sends to assignees. If you're talking about adding a "variable" to this, then the answer is "no" - there is no way to customize the email beyond controlling the task's display name, and whatever assignee(s) the task is assigned to (which will be the same as the email recipients).
You can stop the "Notify task assignees of new task via email and mobile push notification if applicable" and use custom notification where you can add this.
.... and do without notifications in case of a reassignment.