TLDR
df.loc[(level_1_indices_list, level_2_indices_list), :]
which is, in this case:
df.loc[(['California','Texas'], ['2010']), :]
Below is a more elaborated version.
# import packages & set seed
import numpy as np
import pandas as pd
np.random.seed(42)
Create example dataframe
Using the Pandas docs:
arrays = [np.array(['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux']),
np.array(['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'])]
s = pd.Series(np.random.randn(8), index=arrays)
df = pd.DataFrame(np.random.randn(8, 4), index=arrays)
This will look like:

Slicing using multiindex
With df
you can do:
df.loc[(['qux','foo'], 'one'), :]
For notational consistency you can use []
on the second element of the slice:
df.loc[(['qux','foo'], ['one']), :]
which will yield the same result.
Which is:

(Selecting 'one'
is equivalent to selecting 2010
in your df
. ['qux','foo']
should be equivalent to selecting ['California','Texas']. Based on this, I think you can apply the steps here to your data.)
This might also be helpful.