Summarize:

Most clotheslines are approximately 6 ft. tall. Two 10 ft. posts work well for this, because it gives you the height and allows 3-4 ft. of the post to be buried underground. You can also use a 8-8 1/2 ft. post instead. If the posts are too long, you need to cut them. However, these two posts may not need to be cut at all.  If you live in a climate that experiences a deep freeze in the winter, make sure to put your posts below the freeze line so they don't shift. Decide if that is 3 or 4 ft. or more.  You may also need to bury the post deeper in the ground if you live in an area with sandy or unstable soil. Take the two 8 ft. posts and cut them in half. This will give you four 4 ft. posts. Then take two of the 4 ft. beams and cut them in half so you have four 2 ft. beams. These will be used for the cross braces.  That should give you one 4 ft. crossbeam and two 2 ft. braces for each clothesline post. Cut 45 degree angles into the ends of the 2 ft. beams. To do this, adjust your miter saw to the 45 angle. These beams will be the braces. Make sure you double check your angles before cutting the wood. Messing up the angle means you will have to get another piece of wood. The crosspiece can be around 3 ft. long if you want. You can also cut the ends of the crosspiece at an angle if you don't want flat edges. Measure and mark the center of the crossbeam and the center of the top of the post. The center mark will be on the edge of the crossbeam at the top that faces the sky. The center mark on the post will be on the top, which is the edge that the brace sits on. Drill a hole that is a little narrower than the lag bolt in the center where you made your mark.  Connect the crossbeam to the post with the lag bolt. When complete, the crossbeam will sit on top of the post, in the shape of a T. Fit the braces against the post and crossbeam. You want to drill the holes near the bottom at an angle so it will connect to the post, and then through the top so it will connect to the crossbeam and brace. Drill holes into these areas, making sure the hole is centered on the wood.  The braces will fit snugly against the beam and post because of the angle you cut into each end. Clamp the wooden braces in place to stabilize them. Drill the holes into the beams and screw in the bolts. Measure the spaces for your eye hooks evenly along the crossbeam. Make sure not to start at the very edge. Try starting around 6 inches from the edge. For 4 hooks, you want to space them 10-12 inches apart. Pre-drill the holes, and then twist the eye hooks into the holes.  You can use the handle of your screwdriver to twist the hooks into the wood. You may want to install 3 eye hooks instead of 4 depending on the length of your crossbeam.
Measure the posts. Cut the angles in your crossbeams. Drill the holes. Screw the braces to the posts. Install the eye hooks.