I want to make a graph with matplotlib.

Am I correct in understanding that you would like to draw 6x6 (36 points in total) on one graph?

If so, I think we can simply put pyplot.legend() or later out of loop.

 from matplotlib import pyplot
For y in range (6):
    x = [1, 2, 3, 4, 5, 6]
    y1 = [y, y, y, y, y, y]
    pyplot.scatter(x,y1,c='b',label='test_data')
pyplot.legend()
pyplot.title('test')
pyplot.show()

The scatter part is the output part of the graph, so I think it's better to take it out of the for statement.
y ranges from 0 to 5 by adding repeated results to the list each time.
After creating an empty list (y1), add a value of y to the list in append.

import matplotlib.pyplot as plt
x = [1, 2, 3, 4, 5, 6]
y1 = [ ]
For y in range (6):
    y1.append(y)
plt.scatter(x,y1,c='b',label='test_data')

plt.legend()
plt.title('test')
plt.show()

I've changed it to a more general way of writing on Matplotlib.
I hope it will be helpful.