Gather your tools and wood. Leave two of the 4x4 posts 8' long and cut the third post into two 3' sections, leaving 2' of offcuts. Measure 3-1/2" from the top of the 8' posts and draw a line. Using a circular saw, set the blade depth at 1-3/4 " and cut the line drawn until it has been scored. Using a hammer, hit the scored end, knocking the chunks away from the post to create a half lap. A chisel can be used to clean up any unevenness, being careful not to take it past 1-3/4".
Moving to the 3 4x4 posts, measure from the top 18", draw a line. From the measured center line, measure 1-3/4" from both sides. Using the circular saw, score the post just as was done on the 8' posts. Knocking out the waste creating the other half of the half lap. The two poles will slide together, creating a T.
Drill 4 1/4 " holes, at the intersection of the two pieces, and install three inch lag screws with flat washers. Measure 2" from each end of the 3' posts, drill a hole and install two 1-1/2" eye bolts; this will be used to attach the clothesline wire.
With your posthole digger, dig a two-foot deep hole. Measure the distance of the desired length between the poles and dig a second hole. Set the posts in the holes with the eye bolts facing each other. Make sure that the posts are level in both directions. Pour the dry quick-setting concrete mix into the holes and use a garden hose to add water; there is no need to premix.Poke a long sturdy object such as a rod or piece of re-bar into the concrete as you add the water, and after the concrete has set, backfill the hole if needed with the dirt.
Use 2x4 leftover lumber to brace the posts until concrete is set (recommended 24 hours). Install the clothesline rope by tying to first eye-hook, stretching line down to the other pole and tie off at desired tension.Wash clothes and hang out your laundry.