Assuming the contaminants are always separated by commas in your data, you can use pandas.Series.str.split() to get them into lists. Then you can get them into distinct rows with pandas.DataFrame.explode(), which finally allows using the value_counts() method.
For example:
import pandas as pd
data = pd.DataFrame({'File Number': [1, 2, 3, 4],
                     'CONTAMINANTS': ['ACENAPHTENE, ANTHRACENE, BENZ-A-ANTHRACENE', 
                                      'CHLORINATED SOLVENTS', 
                                      'DIESEL, GASOLINE, ACENAPHTENE', 
                                      'GASOLINE, ACENAPHTENE']})
data
    File Number     CONTAMINANTS
0   1               ACENAPHTENE, ANTHRACENE, BENZ-A-ANTHRACENE
1   2               CHLORINATED SOLVENTS
2   3               DIESEL, GASOLINE, ACENAPHTENE
3   4               GASOLINE, ACENAPHTENE
data['CONTAMINANTS'] = data['CONTAMINANTS'].str.split(pat=', ')
data_long = data.explode('CONTAMINANTS')
data_long['CONTAMINANTS'].value_counts()
ACENAPHTENE             3
GASOLINE                2
DIESEL                  1
ANTHRACENE              1
BENZ-A-ANTHRACENE       1
CHLORINATED SOLVENTS    1
Name: CONTAMINANTS, dtype: int64
To categorize the contaminants, you could define a dictionary that maps them to types. Then you can use that dictionary to add a column of types to the exploded dataframe:
types = {'ACENAPHTENE': 1, 
         'GASOLINE': 2,
         'DIESEL': 2, 
         'ANTHRACENE': 1,
         'BENZ-A-ANTHRACENE': 1,
         'CHLORINATED SOLVENTS': 3}
data_long['contaminant type'] = data_long['CONTAMINANTS'].apply(lambda x: types[x])
data_long
    File Number     CONTAMINANTS            contaminant type
0   1               ACENAPHTENE             1
0   1               ANTHRACENE              1
0   1               BENZ-A-ANTHRACENE       1
1   2               CHLORINATED SOLVENTS    3
2   3               DIESEL                  2
2   3               GASOLINE                2
2   3               ACENAPHTENE             1
3   4               GASOLINE                2
3   4               ACENAPHTENE             1