`\sqrt{4+2\sqrt3} - \sqrt{4-2\sqrt3}`

`=\sqrt{(\sqrt3+1)^2} - \sqrt{(\sqrt3-1)^2}`

`=|\sqrt3+1| - |\sqrt3 -1|`

`=\sqrt3 +1 - (\sqrt3-1)`

`=\sqrt3+1- \sqrt3+1`

`=2`