Explanation : Record Route is an optional field used to record address.
In IPv4 header, 40 bytes are reserved for OPTIONS. For Record Route to stores, 1 byte is used to store type of option, 1 byte for length and 1 byte for pointer. Out of 40, 37 bytes are left.
An IP4 address takes 32 bits or 4 bytes.
We can store at most floor(37/4) = 9 router addresses.
Alternate Solution
In IPV4 frame format there are 40 bytes of option field, out of which only 38 bytes can be used, 2 bytes are reserved. Also one IPV4 address is of 4 bytes
Thus maximum IPV4 address that can be hold <= 38/4 = 9