How many animals?

Only one, as far as we can tell. Only the rabbit was going into the river. That the rabbit saw the elephants while going into the river says nothing about what the elephants were doing, and the monkeys going toward the river does not necessarily imply that they went into it.

Who on earth composed this stuff? It is the most incompetently written question that I have ever seen. It should certainly not originate from any math course (at least I would hope so). Math is about being precise. If the question itself is nonsensical, then no answer is possible.

The question is terrible English as well. It nowhere makes clear exactly WHO is "going towards the river". Is it the rabbit? Or the elephants? Did the elephants all see the same two monkeys, or different ones ?

I will not waste time trying to make sense of this rubbish.

There are several solutions, depending on whether the elephants all saw two different monkeys or they all saw the same two. It also depends on whether the elephants went to the river.

1 rabbit saw 6 elephants while going to the river.

1r + 6e

Every elephant saw 2 monkeys going toward the river.

6 x 2m = 12m

or

1 x 2m = 2m

Every monkey holds 1 parrot in its paws.

12 x p = 12p

or

2 x p = 2p

1r + 6e + 12m + 12p = 31

or

1r + 6e + 2m + 2p = 11

or, if the elepants didn't go:

1r + 12m + 12p = 25

or

1r + 2m + 2p = 5

Well if you're going on the assumption that all the animals are heading towards the river (as it does state "saw... going toward the river").

6 elephants × 2 monkeys = 12 monkeys

12 monkeys × 1 parrot = 12 parrots

12 monkeys + 12 parrots + 1 rabbit + 6 elephants = 31 animals in total.

1 rabbit + 6 elephants + 2 monkeys + 2 parrots = 11 animals.

It doesn't say that each elephant saw 2 monkeys. Therefore there were only 2 monkeys going toward the river. The word "while" is ambiguous because it's not clear whether it refers to the rabbit or the elephants. Thus there are two possible solutions.

5 as it's stated the elephants didn't go.