Newer versions of matplotlib (e.g. 3.7.0) doesn't require explicit date2num calls anymore. Just pass a point on the plot directly as xy= to annotate().
from datetime import datetime
import matplotlib.pyplot as plt
x = [datetime(2009, 5, 1), datetime(2010, 6, 1),
datetime(2011, 4, 1), datetime(2012, 6, 1)]
y = [1, 3, 2, 5]
fig, ax = plt.subplots(facecolor='white')
ax.plot(x, y, linestyle='--')
ax.annotate('Test', xy=(x[1], y[1]), # <---- directly pass the point position
xytext=(-15, 15), textcoords='offset points',
arrowprops={'arrowstyle': '->'})
fig.autofmt_xdate()
A more terse (but less flexible) solution is to use text() to annotate. Again, no need to perform a datetime-to-number conversion; just pass the point as is.
plt.plot(x, y, linestyle='--')
plt.text(x[1], y[1], 'Test') # use x-y coordinate values as is
plt.xticks(plt.xticks()[0][::2]);
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