Double-hung windows slide up and down to open and close. Double-hung means both the top and bottom sash open. When you are installing two double-hung windows, it is no different than installing one double-hung window two times. Proper measurements of the opening must be taken for each individual window.
Measure the length and width of each rough opening. Run a tape measure from one end to the other of both openings and record the measurements so the proper size windows can be installed. These measurements will generally be the same for side-by-side windows.
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Put a tube of silicone sealant into a caulk gun. Cut off the end of the sealant with a utility knife and run a bead of caulk along the window opening from the inside of the house. Spread out a thin bead up each side and across the top. Repeat the process for the window on the other side.
Set the first window into the opening so it can adhere to the caulk. Insert a screw through the side of the window and into the jamb on both sides with a power drill. Space out the screws every six inches up each side and insert them until they are flush with the jamb on the side of the window. Repeat the process for the other window.
Set a level vertically on the window and verify the window is square and plumb. Insert shims between the jamb and the window, if necessary until it is level. Cut off the excess shims with a utility knife. Repeat the process for the other window.
Run a bead of caulk along the outside of the house to seal the opening. Squirt a thin bead along the entire perimeter of both windows. Open and close the windows and verify they are working properly.