You may be getting confused regarding the "Sunny 16" rule which suggests that a correct exposure would occur in mid-day sun if you set the f-stop to f/16 and you set the shutter speed to the inverse of the ASA or ISO.
That's just a baseline used specifically because f/16 is the only f-stop at which the shutter speed is the simple inverse of the ASA or ISO. Basically the rule (a) works and (b) is very easy to remember. But this is just one way to combine the shutter speed and aperture setting and ASA or ISO to get the correct amount of light. Any combination of of ASA or ISO with aperture and shutter speed that gets the equivalent amount of light will ALSO work.
Suppose you use f/8 instead of f/16. f/8 is actually two stops brighter than f/16. Let's start with f/16 and work from there...
If you were to initial dial in the "Sunny 16" exposure with 400 ASA film then you'd be at f/16, 1/400th.
But there is a shutter speed caveat. You can't necessarily just dial in ANY shutter speed because that setting might not appear on your dial. The order of full shutter speeds starts with 1 full second and then each step up halves the time (at a few points there's a round-off to keep the math easy). So that means the order is: 1/1 (1 full second) then 1/2, 1/4, 1/8, 1/15 (notice the slight adjustment because it's not 1/16), then 1/30, 1/60, then 1/125 (notice another adjustment because it's not 1/120) then 1/250, 1/500, 1/1000, etc.
So while 1/400 isn't on the dial (it is on a digital camera - they typically allow adjustments in 1/3rd stop increments instead of full stops or half-stops)... 1/500 is on the dial and that's the closest to 1/400. It's close-enough that the slightly faster shutter speed (1/4 of a stop) won't have a dramatic effect on your exposure and you can easily compensate for this when making prints.
Now to do this at f/8... you've opened up the aperture by a full 2 stops. Each 1 full stop doubles the amount of light... so if we double, then double again, the area increases enough that we actually collect four times more light. So we'll need to adjust the shutter speed to compensate by allowing the shutter to remain open 1/4th as long. This means instead of using 400 ASA with f/16 and 1/400 (and we had to use 1/500 because 1/400 isn't on the shutter speed dial) you'd use f/8 with 1/1600... and again... take whatever speed is nearest on the mode dial. And this might create a NEW problem... does your camera actually have a shutter speed that fast?
Many old cameras top-out at 1/500th... or maybe 1/1000th. I'm going to guess that your camera can't support 1/2000th and this will force you to use the higher f-stop.
But even if your camera did support the faster shutter speeds... the only f-stop at which the shutter speed is simply the inverse of the ASA is at f/16. Notice in the example above (the f/8 example) that the shutter speed is quadruple the ASA setting. That makes the rule harder to remember. f/16 is selected because it works for most any camera AND because the rule is easy to remember. But this just gets you to the base exposure... you can still trade shutter speed stops for aperture stops... or swap film to a different ASA rating which changes by stops of film sensitivity (although changing film isn't as convenient and most people won't unload a roll until they've shot the entire roll.)
Shutter speeds are doubling or halving the amount of light that can pass through simply by doubling or having the TIME the shutter is open.
Aperture values are doubling or halving the amount of light that can pass through by simply doubling or halving the geometric AREA of the aperture opening (it literally is the mathematical calculation of the area of a circle... remember area = π x r^2
You can think of an analogy such as filling a glass of water at the tap without over-flowing the glass. You can turn on the spigot to a slow trickle and wait a long time for the glass to fill... or you can crank open the spigot to full-blast and it'll get full much faster. Its your choice as long as you find a way to (a) fill the glass and (b) not over-fill it.