Because the Duma (parliament) rejected Chernomyrdin, President Yeltsin has one week to submit a new nomination. He may either renominate him or select another candidate. He is expected to renominate him.
The Duma has one week from the day the new nomination is submitted to consider and vote on it.
If it votes down Yeltsin's candidate or candidates three times in a row, the president must dissolve the Duma and call elections. They must be held within four months. He may then appoint whomever he chooses to be prime minister.