Because spot convention is yen per dollar and the future is dollars per yen, a rising 6J means a falling USD/JPY. Traders moving between the two markets routinely get the direction backwards the first time.
The quote itself is unusual, typically shown as 0.006750 or in some platforms as 6750 with an implied decimal. Contract notional is the quote times 12,500,000, and the minimum tick of 0.0000005 is worth $6.25.
Example: 6J at 0.006750 is a notional of $84,375 per contract, equivalent to USD/JPY at 1 / 0.006750 = 148.15. If USD/JPY falls to 145.00, 6J rises to 0.006897 and a long gains (0.006897 - 0.006750) x 12,500,000 = $1,837.
Related: currency-futures, euro-fx-futures, carry-trade, major-pairs, quote-currency