When a number is divided by 7 and 9 , the remainder is 4 and 3. what will be the remainder of a same no. when it is divided by 37.

numbers which, when divided by 7 , leave a remainder of 4:

11 18 25 32 39 46 53 60 67 74 ...
numbers which, when divided by 9, leave a remainder of 3:
12 21 30 39 48 57 66 75 ...

looks like 39 is the first such number, there are an infinite number of them, they are

39 102 165 228 ... (adding 9x7 or 63) each time
I will assume you want the smallest such number

39 ÷ 37 = 1 and 2 left over