When I mix blue and yellow in Inkscape, I get gray.
How can I instead get green, like you would see when mixing crayons or paint?
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Inkscape is an RGB application, designed for making SVGs and graphics for display on the web in web browsers, which also use RGB colours, as do computer screens.
Crayon colours (and paint/inks) use a subtractive colour system, they work by absorbing and reflecting light, so they don't work the same as RGB colour which is an additive colour system which emits light.
In the RGB colour model red and green make yellow. This may seem unintuitive, but it's the way the physics of light works. This can be seen in Inkscape by setting the overlapping object blending modes to "Difference".
You can kind of force Inkscape to mix blue and yellow to get green, however the blue you chose is too dark. You can set the yellow object to have a "Multiply" blending mode in the Objects panel.
Here's the result, which is a kind of muddy green. If you use an even lighter blue like cyan, you would get a brighter green.
If you are interested in learning more about how colour works, check out this link which discusses additive versus subtractive colour.
Edit: In case you just want a green overlap and don't really care about it being created with blending modes, then it is entirely possible to fake it in Inkscape.
This example has a shape created by using the boolean operation "Intersect", copying the resulting shape, undoing using CTRL+Z, then pasted in place, on top of two circles, and just set to a green fill.