Solution:
As per the question,
All the telephone numbers have 6 digits
Provided that,
First 2 digits = 41 or 42 or 46 or 62 or 64
As a result, the no. of two digits that the telephone no. begins with =5
The first 2 digits can be filled in five ways,
The remaining four-digits can be filled in ${ }^{8} \mathrm{P}_{4}$ ways,
${ }^{8} \mathrm{P}_{4}=8 ! /(8-4) !=1680$
As a result, no. of telephone nos. having 6 distinct digits $=5 \times 1680$ $=8400$