The mode selector for Pajero is very well documented by @Frederic which also explain the technicalities. Personally, it does not bother me anymore of not being able to climb Faya (though i still try 😉) and not do things that other cars are doing. I completely understand you @Mehmet Volga, but I feel the Pajero is a very capable car but it has its limits due to the weight, engine and gearing.
I do-not think, the Pajero will climb better on 4HLc because i did try it few times. Actually, 4H is better to gain momentum to climb.
By default, I always offroad on 4H and I use HLc only when i see a very soft or churned up area where the chance of stuck is high. I personally think that since the 4H distributes more power to the rear wheels than the front wheels, the car's rear wheels tend to dig in easily on soft patches and the front wheel does not have enough power to pull the car out.
However on HLc, since the power is distributed equally to both rear and front wheels, the traction is well balanced and the car floats better in super soft sand with lesser chance of sinking.