hakko no tamago / tamago ga hakko

  • The first one would be the noun phrase "(the) Eight Eggs", and the second one would be the sentence "(There are) 8 eggs", though at the end you better put あります at the end.
    Both forms are admissible, although the second one is preferred, I think; actually, the natural position for numerals in the Japanese sentence is just before the verb, after all other complements. For example:

    Kodomoga san-nin arimasu.
    (He/she) has three children.

    Kyonen kaishaha kurumawo godai kaimashita.
    Last year, the company bought five cars.

    So the が is variable -- with います/あります, you'd use が, but with other verbs, you would use the particle appropriate to the last verbal complement, whichever it is. If, for whatever reason, the numeral cannot be near the verb, typically because there is more than one set of numerals in the same clause, it can go near the object it modifies separated by a の, like in the first form.
    Thank you Noamoxkaltontli. That is why I was asking. I learned from another website that the proper way to use counters is "item + ga + counter + arimasu / imasu. But the two examples above were exactly how RS had it. They did also have it in another example the correct way with the arimasu. Not sure what point RS was trying to make, but thank you for the clarification.
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