As well explained here there are the following two ways to set a Windows 10 PC/tablet work in tablet mode (that is with the best user interface if you are using a touch interaction and not a mouse & keyboard one):

• Go to Settings -> System -> Tablet mode and then enable the related available switch.
• Use the Tablet mode button, available in the Action Center.

However, it could happen that using both those available methods, the Tablet mode cannot be enabled because the button/switch is greyed so it is not possible to interact with it.

Settings -> System -> Tablet mode

Tablet mode button available in the Action Center

The matter is because you are working with multiple displays and, in particular, setting the Extend option in order to see different things on each display: this is the only situation that does not allows to switch to Tablet mode, while all the others (PC screen only, Duplicate, Second screen only) let that option able to be possibly set.

This seems to be logic if you think (e.g. if you are doing for example a presentation and you are connected to a projector, if you want to use the PC in Tablet mode to show something, you surely will choose the Duplicate screen option in order to project what are you doing acting on the PC touchscreen), but may be, the for time, it can surprise you if you usually work with two screens set in Extend mode!!