Numbers are to be formed between 1000 and 3000 , which are...

To find total numbers between $1000$ and $3000$ divisible by $4$ using the digits $1, 2, 3, 4, 5, 6$,

We will solve in two cases.

Case I : When first digit is $1$.

Then last two digits can be $24, 32, 36, 52, 56$ or $64$

So, total ways of choosing last two digit is $6$ and second digit will be chosen in $3$ ways

So, number of such numbers $= 6 \times 3 = 18$

Case II: When first digit is $2$

Then last two digits can be $16, 36, 56$ or $64$

So, total ways of choosing last two digit is $4$ and second digit will be chosen in $3$

So, number of such numbers $= 4 \times 3 = 12$

Total numbers of numbers $= 18 + 12 = 30$