"US Letter size" is 8x11 inches. If you are using 8x10 stock, you may have to create a new Page size, or you could use US Letter and take care to place nothing in the bottom inch of the page (Portrait orientation) or right side of page 1 and left side of page 2.
Set up and print a Test sheet first.
Open a blank Page Layout document. Set its four margins to zero.
Insert a Text box onto the page. Adjust its size to 4" by 5", and set a black boundary.
Duplicate the original three times to create four identical Text Boxes.
Arrange the four to touch the top, left, and right edges of the paper, and to touch the adjacent box beside it and the adjacent box above or below it.
At this point, your document should contain a single set of four panels into which you will place the content you want.
Duplicate the page.
On the First page, enter the a single letter in each box, following this pattern:
A B
C D
On the second page, enter one of the same four letters in the boxes, following this pattern:
B A
D C
Using your printer's 2 side printing, print a test sheet containing page 1 on one side of the paper and Page 2 on the other side.
You should find that each of the four letters is on the front and back of one box, and that the boundaries of the boxes are aligned if you place a light behind the sheet. f not, take note of the adjustments needed to make it so, make those adjustments, and print a new test sheet.
When the alignment is satisfactory, save the document as a template.
If the end result is not what you are looking for, please post an image of the two sides of the paper (including the test text), and describe what chages are needed.
Regards,
Barry