To slice the outer index level of a pandas DataFrame or Series with a multi-level index, you can use the .loc method with a tuple of slice objects. The slice objects define the range of values you want to select for each level of the index.

Here's an example:

import pandas as pd
 
data = {'Value': [10, 20, 30, 40, 50, 60],
        'Year': [2019, 2019, 2019, 2020, 2020, 2020],
        'Quarter': ['Q1', 'Q2', 'Q3', 'Q1', 'Q2', 'Q3']}
df = pd.DataFrame(data)
df.set_index(['Year', 'Quarter'], inplace=True)
 
# Select all rows where the Year is 2019
subset = df.loc[(2019, slice(None)), :]
 
print(subset)

In this example, the df DataFrame is created with a multi-level index composed of the Year and Quarter columns. We then set this index using set_index(). To slice the outer index level and select all rows where the Year is 2019, we pass a tuple containing (2019, slice(None)) to .loc. The slice(None) is used to select all possible values for the Quarter level of the index.

The resulting subset DataFrame is:

            Value
Year Quarter      
2019 Q1        10
     Q2        20
     Q3        30

Note that we selected all columns in this example using the : slice notation. You can also select specific columns by passing a list of column names or positions to .loc.