This is another example of a really badly constructed question!
It has no clear answer. You could say 'along' 'across' or 'on'.
You could say "He is walking across the zebra crossing" to mean that he is walking across the road by using the zebra crossing, even though this is ambiguous. If you are being pedantic, 'walking across the zebra crossing' might not actually mean that you are crossing the road - it means that you are walking a metre or so along one of the black or white stripes ( a very odd thing to do!). We say 'walking across the zebra crossing' in the same way as we say 'walking across the bridge', even though this is rather illogical. In fact, it's the road or the river that we are going 'across' - the zebra crossing and the bridge are actually the means of going across these things.
In terms of direction, walking 'along' the zebra crossing is more correct. If the zebra crossing is a metre wide and ten metres long, when you cross the road, you are going 'along' zebra crossing because you are walking along the length of it. But in practice, we never say this. You walk along a path or a road, but not a zebra crossing. Zebra crossings aren't really very long, and nobody spends much time on them.
You can also say 'Walking on the zebra crossing'. This just says where you are e.g. 'It's safer to walk on the zebra crossing than on the road'.
The more you think about this question, the worse it gets. I suspect that whoever wrote it wanted you to put 'across', but it's not a typical (or even correct) use of the word 'across', and it won't teach you how to use across in other situations.