∵a=√7-1
∴a+1=√7
∴a²+2a+1=7
∴a²=6-2a
∴3a³+12a²-6a-12
=3a(6-2a)+12a²-6a-12
=6a²+12a+12
=6(6-2a)+12a-12
=36-12
=24