Unlike some Adobe Illustrator tutorials, this one gives you two ways to do the same thing. In case you would like to use a different method for creating a checkerboard pattern, here's how to do it using the "transform" effect.
1. Draw a red square. Select the rectangle tool, click on the canvass and create a red square that is 100 px x 100 px. Give the square a black stroke.

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2. Add a black square. Select your square and then - while holding the <Alt> key down - drag it to the right. If you have "Smart Guides" enabled, the second square should snap to the right of the first. Fill the second square with black.

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3. Create your first row. Select both squares and then click "Effect", "Distort & Transform" and then "Transform". In the "Transform Effect" window, under "Move", enter "200 px" in the "Horizontal" field (because both squares together are 200 px). In the "Copies" field, enter "3". Click the "OK" button to finish the row.

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4. Create the second row. Follow the procedure above to create a second row that begins with a black square and has a red square to the right of it.

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5. Fill out the checkerboard. Select the four squares and then click "Effect", "Distort & Transform" and then "Transform". In the "Transform Effect" window, under "Move", enter "-200 px" in the "Vertical" field (because both rows together are 200 px). In the "Copies" field, enter "3". Click the "OK" button to finish the row.

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6. Expand appearance (optional). With your four squares selected, click "Object" on the menu bar and then "Expand Appearance." You can now manipulate each square individually.