- My laptop touchpad supported multitouch gestures on windows, but not Linux.
libinput list-devices
<SNIP>
Device: AlpsPS/2 ALPS DualPoint TouchPad
Kernel: /dev/input/event24
Group: 10
Seat: seat0, default
Size: 80x44mm
Capabilities: pointer
Tap-to-click: disabled
Tap-and-drag: enabled
Tap drag lock: disabled
Left-handed: disabled
Nat.scrolling: disabled
Middle emulation: enabled
Calibration: n/a
Scroll methods: *two-finger edge
Click methods: none
Disable-w-typing: enabled
Disable-w-trackpointing: enabled
Accel profiles: flat *adaptive
Rotation: n/a
I can use only two fingers (POINTER_SCROLL_FINGER)
Have you ever said to your wife that your mother cooked better? 
If you really don’t want an answer, leave this in the title:
" It was working on windows"

I’m so sorry, I said “it was working on windows” to indicate that my touchpad supports multitouch, and it’s not a hardware issue.
I hate windows and I will not use it again, I’m using Linux for 2 years since I know it.
It may not be so much the touchpad driver but the window manager or desktop environment support for gestures and the ways to configure them.
I found this:
libinput - ArchWiki
the whole article, but especially the section 3.5 and the following
Then there is the option to use the synaptics touchpad driver instead of libinput:
Touchpad Synaptics - ArchWiki
I rarely use my touchpad and never cared about gestures, so this is all just theoretical “knowledge”.
I read the whole article trying what is recommended, I found Synaptics is deprecated and not supported.
libinput working properly only with two fingers, so any gestures software (touchegg, fusuma, libinput-gesutres, etc.) does not receive any swipe signal
I already said that my “knowledge” is only theoretical.
But:
again from the very start of this site
Touchpad Synaptics - ArchWiki
That’s not what it says.
It says (the red box)
Warning: xf86-input-synaptics is no longer actively updated. If possible, use libinput. For some reasons why you might still prefer xf86-input-synaptics, see, e.g. [1] and [2].
That, to me, is not the same as: depreciated and not supported
But then there is the blue box right below that red box:
Note: If you want to configure touchpad via GNOME Settings, you need to use the libinput driver.[3]
Which means (to me) that there is no point in using synaptics - not when you are on Gnome, that is.
I have no solution or informed and tested advice to offer. 