Why not "itt vagy ott"? And to translate "ide vagy oda", why not "to here or to there"?
“To here” is wrong in English¹, and the word “here” remains unchanged in the face of a movement towards it: “I am coming here”, and NOT “I am coming to here”.
“There are a number of common words in English, such as here, there, home, up, down, upstairs and downstairs which are not preceded by the word to.”¹
However, in Hungarian, the movement needs to be shown in the adverb. While "here" could be correcly translated to either "ide" or "itt", hence “I am coming here” could (grammatically) be either “Itt jövök” or “Ide jövök”, the first one does not make much sense, because there would not be any direct link between the words "itt" and "jövök". This way, we are left with only one option: “Ide jövök”.
In the exercise, there is a “hova” at the beginning of the sentence, which implies movement. For this reason, even if the verb referred to an action with no movement; solely because of "hova" one must admit only the meaning where the action has movement, and also foresee an adverb expressing such movement. In this case, “Ide” or “Oda”.
P.S: I believe the verb “lép” can refer to an action without movement, under other circumstances, but that in such case, it would change the meaning from “step” to “perform”/”take action”:
“Egyértelmű, hogy Hitler hamarosan lép valamit Lengyelország ellen.”
"To here" and "to there" are technically correct, but it doesn't seem to be used much. At least not in American English - British English might be different.
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