How to create a count plot for a nested dataframe in matplotlib

Before starting on the visualisation, I would suggest re-shaping your data to make the nesting levels explicit and pre-calculate the frequencies. Something like:

import pandas as pd
import matplotlib.pyplot as plt
import matplotlib as mpl
import matplotlib.gridspec as gridspec

temp_df = pd.concat([
    df.groupby(["a"])["b"].value_counts().reset_index(name="count").rename(columns={"b":"value"}).assign(level_2="b"),
    df.groupby(["a"])["c"].value_counts().reset_index(name="count").rename(columns={"c":"value"}).assign(level_2="c")
])

final_df = (temp_df
            .rename(columns={"a":"level_1"})
            [["level_1", "level_2", "value", "count"]]
            .sort_values(["level_1", "level_2"]))

The resulting dataframe will look like this:

   level_1 level_2  value  count
0        0       b      3      2
1        0       b      7      2
2        0       b      1      1
0        0       c    -50      2
1        0       c    102      2
2        0       c     30      1
3        1       b      2      1
4        1       b      3      1
3        1       c     10      2

Now to plot values and their counts in this nested way, you can use GridSpec to define the layout based on how many values fall under each nested level. I've hard-coded the values for the purposes of illustrating this toy dataset, but you'd want to handle this programmatically for your real data.

You have 9 values so the GridSpec will have 9 columns. You have 2 nested levels, so we reserve 2 bottom rows for nesting labels and add a few more rows to "host" the bar charts.

f = plt.figure(figsize=(10,4), dpi=300)

grid = gridspec.GridSpec(10, 9, figure=f)
mpl.rcParams["axes.edgecolor"] = "gainsboro"

# Use context manager to set mpl parameters for nested axs
with mpl.rc_context({"xtick.major.bottom": False, "ytick.major.left": False}):

    # Level 1 axs (label, ax)
    ax_level_1_0 = ("0", f.add_subplot(grid[9, 0:6]))
    ax_level_1_1 = ("1", f.add_subplot(grid[9, 6:]))
    level_1_axs = [ax_level_1_0, ax_level_1_1]

    # Level 2 axs (label, ax)
    ax_level_2_0b = ("B", f.add_subplot(grid[8, 0:3]))
    ax_level_2_0c = ("C", f.add_subplot(grid[8, 3:6]))
    ax_level_2_1b = ("B", f.add_subplot(grid[8, 6:8]))
    ax_level_2_1c = ("C", f.add_subplot(grid[8, 8:]))
    level_2_axs = [ax_level_2_0b, ax_level_2_0c, ax_level_2_1b, ax_level_2_1c]

# Actual count plot axs (level_1, level_2, ax)
ax_0b = (0, "b", f.add_subplot(grid[0:8, 0:3]))
ax_0b[2].set_ylabel("Frequency")

# Hide y-ticks
with mpl.rc_context({"ytick.major.left": False}):
    ax_0c = (0, "c", f.add_subplot(grid[0:8, 3:6]))
    ax_1b = (1, "b", f.add_subplot(grid[0:8, 6:8]))
    ax_1c = (1, "c", f.add_subplot(grid[0:8, 8:]))

count_axs = [ax_0b, ax_0c, ax_1b, ax_1c]

# Remove white space between subplots
plt.subplots_adjust(wspace=0, hspace=0)

# Add label text to Level 1 and 2 axs
for label, ax in level_1_axs + level_2_axs:
    ax.text(0.5, 0.5, label, horizontalalignment='center',
            verticalalignment='center', transform=ax.transAxes)

    
for l1, l2, ax in count_axs:
    y = final_df.query(f'(level_1 == {l1}) & (level_2 == "{l2}")')["count"]
    labels = final_df.query(f'(level_1 == {l1}) & (level_2 == "{l2}")')["value"]
    x = range(len(y))
    ax.bar(x, y, color="steelblue")
    ax.set_xticks(x)
    ax.set_xticklabels(labels)
    ax.tick_params(
        axis="x", direction="in", bottom=False, pad=-20,
        colors="white", labelsize=15)