I'm really bad at physics and would appreciate anyone explaining how you would solve this to me!

Calculate the amount energy needed to completely vaporize a 100 g piece of 20oC gold.

melting point: 1064 degrees C Lf = 64 KJ/Kg
boiling point: 2856 degrees C Lv = 1645 KJ/Kg
c = 0.13 KJ/Kg degrees C

The energy to vaporize gold is equal to the sum of:

1) Energy to heat solid gold to the melting point, which is the temp change from 20 degrees to 1064 degrees times the specific heat constant for gold in its solid phase times the amount of material in Kg, plus
2) Heat of melting, which is Lf times amount of material in Kg, plus
3) Energy to heat liquid gold from its freezing point to its boiling point, which is equal to the temp change from 1064 degrees to 2856 degrees times the specific heat constant for gold in its liquid phase times the amount of material in Kg, plus
4) Heat of vaporization, which is Lv times amount of material in Kg.

This gives you an answer in KJ - what do you get?

By the way, the value for C that you provided seems proper for gold in solid form but may not be appropriate for gold in liquid form - did they give you a different value for that?

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