You can create a subplot with a specification of your own, and then pass the current axis as a parameter. Here I'll create a subplot with 1 row and 2 columns:
import pandas as pd
import matplotlib.pyplot as plt
df = pd.DataFrame({'mass': [0.33, 4.87, 5.97],
'radius': [2439.7, 6051.8, 6378.1]},
index=['Mercury', 'Venus', 'Earth']
)
fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(12, 12))
df.plot.pie(y='mass', ax=axs[0])
df.plot.pie(y='radius', ax=axs[1])
plt.show()
The code above produces the following result:

In case you wanted 6 figures next to each other, set the ncols parameter to 6, and then pass through all 6 axes. Here's a quick demo.
fig, axs = plt.subplots(nrows=1, ncols=6, figsize=(12, 12))
for ax in axs:
df.plot.pie(y='mass', ax=ax) # plots the same pie 6 times

Be sure to read more about matplotlib and how figures/axes work from their documentation.