How to compare columns of one dataframe with the columns of other data frame and write specific row

Question

I am working on pandas project, I am pretty new to it , I have a dataset of two huge dataframe similar to bellow DF's

DF1 :

Data1    Data2      Data3
Head     Cat        Fire
Limbs    Dog        Snow
Eyes     Fish       Water
Mouth    Dragon     Air

DF2 :

 Data1     Data2      
 Limbs     Dog        
 Mouth      Dragon        
 Head      cat        

I have to compare DF2 (Data1 and Data2) with the DF1 (Data1 and Data2),

for ex:

lets say, I pick DF2 first row with combination (Limbs,Dog) this should be searched in DF1 , as we can see the combination exits in the 2nd row , then write DF1's Data3 value "Snow" to the DF2 Data3 value.

Final expected output

Data1         Data2         Data3
 Limbs        Dog            Snow 
 Mouth        Dragon         Air     
 Head         cat            Fire

Currently, I have tried reading the df separately but stuck at compression phase

after_fix = df[['Data1', 'Data2']]

after_fix