If the first weighing of four against four does not produce a balance, then the second weighing involves three against three with balls switched between the two pans and a good ball introduced. So:
A + B + C + D > E + F + G + HWe try
A + B + E against C + F + JIf
A + B + E = C + F + J,then we know that either D is heaver or G or H is lighter, so we weight G against H.
A + B + E > C + F + J,then we know that either F is lighter or A or B is heavier, so we weight A against B.
A + B + E < C + F + J,then we know that either E is lighter or C is heavier, so we weight either against a good ball (e.g. K against E).
An alternative second weighing is A + B + E against C + D + F, which follows similar lines to the above.