Your game can tell you.

Go to coil test, scroll through to that coil. Hit the start button, and then start hitting the + diagnostic button. This steps you through coil, transistor, fuse, connector, WIRE COLORS, etc.

LTG : )

Light brown with yellow stripe goes to the green coil and the brown wire with green stripe goes to the smaller yellow coil. They are indeed small guage wires.

Don't reconnect them without testing the driverboard! My guess is the transistor that drives the solenoid is shorted on. I had this exact same situation with mine. I put a new coil in, hooked it up, smoked the new one.

The power wires are the same for both coils. The reset coil control side is brown and the drop target drop coil (small one) is brown/green. Take note of the side mine are connected to. Yours seems reversed on the reset coil but I not sure if that matters since these do not have a diode

Also - I am guessing those are disconnected for a reason. Put a meter across the both coils lugs one at a time. Of they read 0 ohms they are dead coils

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You'll need a multimeter with a diode test setting. Here's a thread I started at RGP 3+ years ago as a noob.

http://rgparchive-removed.com/rgpforum/showthread.php?t=270509

LTG taking me to school. It has the transistor number to inspect.

These two coils do not have diodes.. Per pinwiki for the coil

13 Testing a coil

If a driver transistor shorts on, it will cause the associated solenoid to activate at full power and stay activated. If the coil wire gets hot enough, it will burn out its plastic coating, shorting the wires and dropping the resistance to near 0 Ohms. If this happens and you replace the broken driver transistor, but you don't check the coil, the shorted coil will cause the transistor you just replaced to be damaged.
If you are unsure of the condition of the coils in a machine it is very wise to check each coil's resistance *before* switching the machine on. The human nose can be a very useful tool in diagnosing when something has burned, so use it!
Some flipper coils are "two coils in one," where they have a power coil and a hold coil. These are normally identified as having three lugs instead of two. You can treat these as two "separate" coils for the purposes of the tests below.

13.1 Testing resistance

To test a coil's resistance:
set your DMM to 'Ohms' and attach your red and black probes to the coil lugs.
If you see a reading of less than 2 Ohms, the coil has either shorted internally or there is a wiring fault. Note: Some flipper coils will read less than 2 ohms but still be fine.
Desolder the wires going to the coil lugs and check the resistance across the coil lugs again. If it reads the same value when disconnected, then the problem lies with the melted coil. If the coil resistance reads 'normal' when it is disconnected (ie the coil is 'ok'), you may have a wiring or driver transistor issue.
It is wise to check all wiring and transistors associated with a melted coil before replacing it and powering on again.

Transistor

http://www.pinwiki.com/wiki/index.php?title=General#Testing_a_Transistor.2C_Silicon_Controlled_Rectifier_.28SCR.29_or_Field_Effect_Transistor_.28FET.29