You can control the aperture by putting the camera in aperture priority mode (Av). Then you set the aperture, and the camera corrects the exposure using shutter speed and/or ISO. If you don't want it to do that either, then put the camera in manual mode. You can also set the ISO manually.
But you need to set your aperture to f/7.1 or narrower (i.e. bigger number, like f/8, f/11, etc.) to zoom without it changing.
Because what you can NOT do is stop the aperture changing when you zoom, if your starting aperture is less than f/7.1. The reason is that the lens simply doesn't have an aperture of f/4 when you're zoomed in; literally, the hole in the lens where the light comes in is physically smaller than that. The reason is that the terminology "f/x" means "focal length divided by entrance pupil"; and with a zoom lens, you are of course changing the focal length.
So f/4, on a 24mm lens (your lens, zoomed out) is 24/4 = 6mm -- the entrance pupil is 6mm wide. (The entrance pupil is where the diaphragm is, basically.) But when you zoom in, if it was still f/4, that would be 105/4 = 26.25mm -- the entrance pupil would be over 26 millimetres wide. And your lens just doesn't have glass bits that big. So, zoomed in, the best you can get is f/7.1, which is 105/7.1, which is close to 15mm. That's the limiting size of your lens' optics when zoomed in.
(Actually it's what your entrance pupil looks like when viewed through the front of the lens... so these sizes aren't literally correct. But that's the idea.)
So if you zoom out and set f/4, then as you zoom in, the f/ number will change, because "f" (the focal length) is changing, all the way to f/7.1. Good news is that this is communicated to your camera, which can adjust shutter speed etc. to keep the exposure right.
If you want a lens with f/4 through the whole zoom range, they do exist, but you'll see that they're bigger, heavier, and pricier.
