You should be aware that many shape operations involving more than 1 object simply won't work across layers. Shape operations typically require that all objects be on the same layer. In some instances, performing some operations (such as grouping) will move objects between layers so the result is all on one layer.
The result below will move everything to the topmost layer.
The art I used is just a black shape with paths on top that have a white stroke. Everything is an individual object, i.e. nothing is grouped. The paths with white strokes are on a layer above a layer containing the black shape.
- Select all
Object > Expand Appearance (If it's available)
Object > Expand (Turns strokes into shapes)
Object > Compound Path > Make
This compound shape is now on the topmost layer, where the white strokes were located.
You may need to then clean up bits where the white extended outside the black area. Select the shape and grab the Shape Builder Tool from the toolbar. Holding down the Option/Alt just click any bits that extend outside the shape....
If you require the stroked paths to remain stroked paths, as opposed to expanding them, an Opacity Mask may work better. It's not possible to create a compound shape with strokes.
See here: How can i trim the artwork