I've been trying to do the 'red shadows' in Illustrator for almost 2 days and I'm stuck. Can someone help? I saw a video that has a similar tutorial but they did it by hand, I don't think this is done by hand. I tried to offset path and cut out with the original object and it's probably the way, I just cannot realize what is the order of the objects
No effect can decide the right red curves for a given shape. Be they shadows or glosses, the 3D form of the brown shape and the light conditions should be known for it. A flat 2D image contains no info of 3D forms. A well trained artificial intelligence tool may guess good ones based on its collected knowledge of the world, but such functionality is not available in common drawing programs. It's your job to see the right places, lengths, curve forms and width profiles.
One tool for getting hints of how to consistently shade flat shapes which are extruded to have some 3D thickness is Photoshop's layer style (effect) Bevel and Emboss. It has a superior advantage over Illustrator's Extrude & Bevel: Freely editable edge profile curves. Find and see some tutorials of the subject. I cannot include one here.
As already said by others, to imitate the red shapes of your example you can make an offset path and separate good parts from it. Clip for ex. with scissors. Before cutting release compound paths and ungroup groups. Otherwise the scissors tool looks like it does nothing. An example:
The brown shape is a single closed shape (actually a compound path) with brown fill, there's no stroke! The offset path idea is not useful if the shape is made of separate pieces or it contains open curves.
In the left an offset path is added - no fill color, purple stroke!
In the middle a curve segment is separated. Other purple parts are now hidden for clarity.
In the right the stroke width is adjusted. One possibility is to use the width tool. To get something fast you can apply an existing stroke width profile. The latter is done in the image above, but it is not exact, because the used preset width profile is symmetric. If you watch carefully your own example you see that the gap between the red curve and the original has a constant width. The red curve doesn't bulge towards the original. My image above is not ok in that sense.
Here's a better attempt:
In the left there's a piece of the brown original and a piece separated from the offset path. In the right there's a non-symmetric purple shape which is used as an art brush. The brush is applied to the separated offset path segment. The non-symmetric brush shape is sliced from a circle by dividing it (Path > Divide objects below) with a straight horizontal line.
Even better control is possible with the width tool. It's tried here:
Insert a width handle in the middle of the curve. Double-click the width handle. The width dialog is opened. Turn one of the side widths to zero.
If you are lucky your preset brush width profile collection contains the needed non-symmetric shape. It's this circle segment:
What you described sounds like the right solution. Offset the path, double click the offset path to isolate it, then use the lasso tool (Q) to manually select the points you don't need and delete, and then change the width profile of the stroke to be tapered.