a)
(\sqrt6-\sqrt7)(\sqrt6+\sqrt7)=(\sqrt6)^2-(\sqrt7)^2=6-7=-1
b)
(\sqrt3-\sqrt5)(\sqrt3+\sqrt5)=3-5=-2
c)
(3\sqrt5+4)(3\sqrt5-4)=(3\sqrt5)^2-4^2=9*5-16=45-16=29
d)
(8-3\sqrt7)(8+3\sqrt7)=8^2-(3\sqrt7)^2=64-9*7=64-63=1
e)
(4\sqrt2-3\sqrt8)(3\sqrt8-4\sqrt2)=12\sqrt{16}-16*2-9*8+12\sqrt{16}=
12*4-32-72+12*4=48-32-72+48=-8
f)
(3\sqrt3+3\sqrt{27})(3\sqrt3+2\sqrt{27})=9*3+6\sqrt{81}+9\sqrt{81}+6*27=
27+6*9+9*9+162=27+54+81+162=324