Any number divisible by 5, its unit place must have 0 or 5. We have to find 4-digit number greater than 6000 and less than 7000. 

So, the unit place can be filled with 2 ways (0 or 5) since, repetition is not allowed. 

∴ Tens place can be filled with 7 ways and hundreds place can be filled with 8 ways.

But the required number is greater than 6000 and less than 7000.

So, thousand place can be filled with 1 digits (i.e) 6,

Th=1; H=8;T=7; O=2  the total number of integers = 1 × 8 × 7 × 2 = 112 

Hence, the required number of integers = 112