Depends on what you are after.
The most straightforward solution is that on image 2 you see two overlapping "rings".
Therefore select one rings inner and outer edge paths, combine them together, add a fill of choice to it.
Do the same with the other two paths.
If they won't produce the inner hole at the rendering, you'd need selecting a node on one of the subpaths -the "loop" you used for combining together, and reverse path direction (>fill rule part of the manual at the fill and stroke panel, Shift+Ctrl+D).
Then, a custom blending mode can composite the two in a somewhat similar manner.
"Screen" is the mostly used rendering mode for such a visual effect.
To pull that off of the hat, you need to add a new layer in the layer panel (Shift+Ctrl+L), create a new layer with the desired blending mode,
select one of the objects and move it to the new layer (Shift+PgUp/Down).
That solution is good for on screen rendering however not so good with printing -as saving as pdf can only preserve the look by creating a raster copy at a set resolution whereas those objects were scalable vectors beforehand.
So if you'd need full vectors -like, for vinyl cutting, would need to go the previously mentioned routes (which also have some downsides and small rendering artifacts you'll eventually run into, even if those details are dealt with by hardly anybody).
