amy tyrone nina jake
Tyrone is next to Jake. Ie: TJ or JT
Nina is next to Mandy. Ie: NM or MN

Two spaces must exist between Tyrone and Nina. So the only options are:
T J M N [ ]
T J [ ] N M
J T [ ] M N
[ ] N M J T
M N [ ] J T
N M [ ] T J

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Only Amy remains and fills in the remaining rows.
T J M N A
T J A N M
J T A M N
A N M J T
M N A J T
N M A T J

Mandy is in line after Jake. So that leaves the following remaining possibilities.
T J M N A
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T J A N M
J T A M N

Amy cannot be first or last in line. So that leaves the following remaining possibilities.
T J A N M
J T A M N

In both situations, Amy, Mandy, or Nina cannot be wearing the orange shirt (because the orange shirt cannot be next to Nina or Mandy).

This means Tyrone or Jake is the orange shirt. Because Jake is the green shirt, Tyrone must be orange.
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And if the first person in line cannot have the orange shirt, the order must be J T A M N.
Jake = green
Tyrone = Orange.

Because the 2nd or 4th person must wear purple, Mandy must be wearing purple.
Mandy = Purple

There are no rules defining which color shirt A or N wears. They can wear red or blue, but not the same colors

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Final order:
J T A M N

J = Green
T = Orange
M = Purple
A = Red or Purple
N = Red or Purple
amy tyrone nina jake