The entire distance of the Appalachian Trail is 2,190 miles in length so if you want to hike the entire Appalachian Trail you'll need at least 7 months to complete the hike depending on how fast you hike and whether or not you take more breaks.
The average person makes the hike at around 3 Miles Per Hour so at 3 MPH hiking speed you can expect it to take up to 7 months to complete the entire hike of the Appalachian Trail.
When hiking the Appalachian Trail your pace is usually slower in the beginning but as you build up your muscle strength you can sometimes start hiking a bit faster.
Some hikers have completed the hike on Appalachian Trail in as little as 50 days but that is very hard to do and most people take the entire 7 months which is nearly a year to complete the hike of the Appalachian Trail.