a) `6\sqrt{12}-5\sqrt{27}+2\sqrt{48}`
`=6\sqrt{2^{2}.3}-5\sqrt{3^{2}.3}+2\sqrt{4^{2}.3}`
`=6.2\sqrt{3}-5.3\sqrt{3}+2.4\sqrt{3}`
`=12\sqrt{3}-15\sqrt{3}+8\sqrt{3}`
`=5\sqrt{3}`
b) `\sqrt{(1-2\sqrt{3})^2}-\sqrt{(4+2\sqrt{3})^2}`
`=|1-2\sqrt{3}|-\sqrt{3+2\sqrt{3}+1}`
`=2\sqrt{3}-1-\sqrt{(\sqrt{3}+1)^2}`
`=2\sqrt{3}-1-|\sqrt{3}+1|`
`=2\sqrt{3}-1-\sqrt{3}-1`
`=\sqrt{3}-2`