You're right to be confused, and you're on the right track with the "weakest link" principle. Let's break down why the stated correct answer (97.5 Amps) is problematic according to the NEC and how we arrive at the correct answer.

Here's the NEC logic

1.

Initial Ampacity (Table 310.16)

2/0 AWG copper THHN has an ampacity of 175 amps at 90°C, 130 amps at 75°C.2.

Termination Temperature Limitation (110.14(C))

This is the crucial part. Because your terminations are rated at 75°C, you MUST use the 75°C column in Table 310.16, even though the conductor insulation is rated higher. This is the "weakest link" principle in action. Therefore, we start with

130 amps.3. Adjustment Factors (310.15(B)(3)(a))

You have 12 current-carrying conductors in a raceway. Table 310.15(B)(3)(a) requires you to apply an adjustment factor to the ampacity based on the number of conductors. For 10-20 conductors, the adjustment factor is 50%.
4.

Adjusted Ampacity Calculation

130 amps (from the 75°C column) 0.50 (adjustment factor) = 65 amps.

Why the given answer of 97.5 Amps is wrong

The stated answer of 97.5 amps is incorrect. You cannot start with the 90°C column ampacity (175 amps) if your terminations are rated lower. This would violate NEC 110.14(C).

Why the 75C Column Answer is also incorrect

You are correct if you use the 75 C column @ 130A with a Derating Factor @ .50 = 65A. This is also incorrect. I will go into more detail in the next part, bear with me it all makes sense shortly!Minimum Circuit Ampacity (MCA) Consideration

Here's where it gets interesting and why the question is potentially poorly worded or has a subtle intention. The question mentions the kilns have nameplates with "MCA" (Minimum Circuit Ampacity) ratings of 136 Amps. Let's dig into this. The NEC requires that the circuit supplying a motor or other equipment be sized to handle the MCA. This ensures sufficient capacity for the load. However, the NEC allows us to use a 90 degree rating and terminate it at 75 degrees, therefore the proper procedure is as follows.

Proper Solution1. Starting point 2/0 AWG Copper with a 90 degree temperature rating @ 175 amps2. Derate based on number of conductors 175 .5 = 87.5 Amps.
3. Increase to meet minimum requirements. Because the MCA is 136 amps we must increase the wire size so we will need to go to 3/04. New wire size 3/0 AWG Copper with a 90 degree temperature rating @ 200 Amps.5. Derate based on number of conductors 200 .5 = 100 Amps.6. Upgrade to 4/0 4/0 AWG Copper with a 90 degree temperature rating @ 230 Amps.7. Derate based on number of conductors 230 .5 = 115 Amps.8. Upgrade to 250 kcmil 250 kcmil AWG Copper with a 90 degree temperature rating @ 255 Amps.9. Derate based on number of conductors 255 .5 = 127.5 Amps.
10. Upgrade to 300 kcmil 300 kcmil AWG Copper with a 90 degree temperature rating @ 285 Amps.11. Derate based on number of conductors 285 .5 = 142.5 Amps.
12. Use the 75-degree C Rating Use the value in the 75-degree C column of Table 310.16.Therefore the correct wire size is 300kcmil with a minimum ampacity of 136 AmpsThe Big Picture and Why This Question is Tricky

This question tests several key NEC concepts:

Termination Temperature Limitations

The 75°C limitation is paramount.

Adjustment Factors

You must adjust for the number of current-carrying conductors.

Minimum Circuit Ampacity

You must meet the MCA requirement specified on the equipment nameplate.

In summary, the question is flawed or intentionally misleading.

Let me know if you want to try some more of those NEC questions. I'm happy to help! Flag for review