ValueError: Must pass DataFrame with boolean values only

You're trying to use a different shaped df to mask your df, this is wrong, additionally the way you're passing the conditions is being used incorrectly. When you compare a column or series in a df with a scalar to produce a boolean mask you should pass just the condition, not use this successively.

def answer_eight():
    counties=census_df[census_df['SUMLEV']==50]
    # this is wrong you're passing the df here multiple times
    regions = counties[(counties[counties['REGION']==1]) | (counties[counties['REGION']==2])]
    # here you're doing it again
    washingtons = regions[regions[regions['COUNTY']].str.startswith("Washington")]
    # here you're doing here again also
    grew = washingtons[washingtons[washingtons['POPESTIMATE2015']]>washingtons[washingtons['POPESTIMATES2014']]]
    return grew[grew['STNAME'],grew['COUNTY']]

you want:

def answer_eight():
    counties=census_df[census_df['SUMLEV']==50]
    regions = counties[(counties['REGION']==1]) | (counties['REGION']==2])]
    washingtons = regions[regions['COUNTY'].str.startswith("Washington")]
    grew = washingtons[washingtons['POPESTIMATE2015']>washingtons['POPESTIMATES2014']]
    return grew[['STNAME','COUNTY']]