How do I move the needle to the right on a singer 7436

Possible thread is wrapped somewhere in the mechanism preventing the machine from moving freely.

...

did you oil moving parts?

here is a link for a free manual, it should have the information in it http://www.singerco.com/uploads/download/1196_7436_ingenuity-manual-(usa)_efs.pdf

have you checked the knob inside the wheel on the right . If not tightened (hand tight) needle will not move.

You don't. You need to purchase a twin needle; it has one shaft, and two needles attached.

First off make sure your bobbin winder is not enguaged, meaning in the left hand position not the right. Also check your handwheel isn't pulled out to the right which would mean your bobbin winding clutch is enguaged.

normally when you use longer thread tails of 4 to 6 inches and move
the thread tails behind the needle before starting to sew.

I am not familiar with Singer 7436. Suggest check the bobbin, remove it and try to turn the machine.
Good Luck,
Bill

a. needle in backwards
or
b. needle threaded wrong

Did you move it to the right?It has to be against the piece above the wheel.