Unless the original flyer is already close to those dimensions or at least in a ratio of 1:2.67, you can't resize it without distorting it horribly or cutting part of it off. You have to set the new file size to 10 X 3 3/4 before you start work on the flyer.
To resize: Image>Resize>Image Size and checkmark the "Resample Using" at the bottom. UNcheck the box immediately above it about maintaining the image ratio/proportions. Now change the width and height values in the Dimensions box and click OK. Take a look at the flyer and click Undo if necessary.
If the original flyer is long and thin, you can increase the size of the canvas around it and then use the Crop Tool with the No Restriction setting. How good it looks will depend on the original ratio of the width to the height and on how balanced the "frame" around it is. (Sounds like too much Math, doesn't it;-) Type in the height and width values and give it a Resolution of 300. (I'm assuming you're printing it. If you're posting it on the web, the Resolution should be 72 and the size will have to be a lot smaller.) Draw a crop boundary around the flyer that takes all of it in then click the Green Checkmark to commit.
To increase the canvas - the empty area around the image - use the Crop Tool set to No Restrictions. Starting in the upper left corner click and drag diagonally to the lower right corner and release the mouse button. If there are any sides where the dashed lines aren't snug against them, snug them up. Now, hold down the ALT key and click and drag one of the corner handles of the Crop Boundary out away from the image at a diagonal. All the sides should move away from the image. If you only need one pair of sides moved out, just click and drag on the handle in the middle of the side. When you release the mouse button you'll see a checkerboard transparent area.
Once the canvas is expanded you can use the Crop Tool to crop the image to 10 X 3 3/4 as explained in the above paragraph.
