Can you take a train from Penn station train to white plains?

No. Trains to White Plains originate at Grand Central/42nd St.

You can walk up to Grand Central (42nd St/Park Avenue), it will take about 20 minutes or take the subway - UPTOWN 1, 2 or 3 train to Times Square-42nd St (one stop), then transfer to the 42nd St Shuttle (S) to Grand Central. Use the staircase at the front of the platform at Grand Central, exit thru the turnstiles, make left then a right. The doors to Grand Central Terminal will be on the left. Fare $2.25