How do you date or find the model of a Belgian made Browning bolt action with serial number 4L24384 if you have tried the website and it does not match anything there?

You have a browning model safari bolt action rifle.These fine rifles were made by FN of belguim.The FN mauser action safari model was made during the years 1959-1975.The 4L prefix dates your rifle to the year 1964.I hope this info helps and answers your questions about this fine made rifle.