I want to buy the
Nikon Zoom-Nikkor 35-105MM 1:3.5-4.5 Lens
I want to know if it is compatible with the Nikon DSLR D3400 camera.
Nikon marketed two versions of the 35–105mm ƒ/3.5–4.5 lens at the same time: a manual-focus version, and an autofocus version.
However, as far as your D3400 is concerned, the distinction doesn't matter. Nikon's autofocus lenses of that time didn't have a focusing motor in the lens; the camera body had the focusing motor to drive the focusing mechanism of the lens.
The D3400 does not have a focusing motor in the body; thus, it will not focus older Nikon autofocus-capable lenses, such as the 35–105mm. The lens is mechanically compatible with the D3400 in that it will mount on the body without damaging either the lens or the body. But you will have to manually focus the lens.
Furthermore, the body is unable to meter through the lens. That means you will have to determine correct exposure before you take a shot. You have to operate your camera in full manual mode with this lens (i.e., select the shutter speed, aperture, and ISO yourself, without the camera picking them for you). But because the camera can't meter through this lens, it can't even tell you if your settings will produce an over- or under-exposed image.