(log6 2)^2+log6 3*log6 12
=(log6 2)^2+log6 3*(log6 3+2log6 2)
=(log6 2)^2+(log6 3)^2+ 2log6 2 *log6 3
=(log6 2+log6 3)^2
=(log 6 6)^2
=1^2
=1