Two possible answers for both math and English.

There is only one common static factor (1 Rabbit and 9 Elephants) after that it is unclear in language (English) and math, as to what actually took place.

Did every Elephant see the same 3 Monkeys, or did every Elephant see (9x 3 monkeys) and were there only 3 Monkeys = (3 x2 tortoises = land turtles) or were there ((9x3) x 2 tortoises ).

Which is why in math, there is a strict order of calculating using symbols or (parentheses) to say in which order to calculate. And why there is miscommunication in language.

"1 rabbit saw 9 elephants while going to the river. Every elephant saw the only 3 monkeys in Africa, going to the river. Each monkey had 1 tortoise in each hand. How many animals are going to the river?"

Now we know for sure there are 9 Elephants plus 1 Rabbit plus the only 3 monkeys in Africa +(2 x 3) Tortoises.

Otherwise, after 1 Rabbit and 9 Elephants -->the next bit has many possibilities.

If you want to use who saw who/whom going to the river, as the basis of solving the riddle. And extract out of the equation the Rabbit and the Elephants, then there are still two possible answers In English or Math.

Either only three monkeys or nine x 3 monkeys, without or without the Tortoises who are not going but being taken to the river.

My reckoning:

1 rabbit going to the river

I understand that where the elephants were going to is not mentioned

27 monkeys going to the river, plus 54 tortoises carried by those

Total: 82

I'm not sure any elephants are going to the river, are they? The rabbits saw the elephants while they (the rabbits) were heading to the river. The elephants saw the monkeys while they (the monkeys) were heading to the river.

I think the elephants are just standing there wondering what's so great about the river?

@Proshanto It's the infamous Tanzanian turtle hurling monkey. They have evolved to have hands perfectly designed for grasping a turtle shell. The size and muscular development in the hands allows them to carry turtles with minimal effort. I think they use them to open beer bottles :)