Any employer, employee, or other person aggrieved by any decision of fact or law by the director as to his, her, or its liability to make contributions or to withhold and pay contributions, or as to the amount of contributions due from or to be withheld and paid by him, her, or it under chapters 39 — 41 of this title, or by any refusal of the director to grant a refund or credit under § 28-40-6, may, either on behalf of himself or herself, or on behalf of his or her employees or other persons aggrieved by the decision, or on behalf of both himself or herself and those employees or persons, within fifteen (15) days after notice of the decision has been mailed to his, her, or its last-known address, file an appeal in writing with the board of review, setting forth the grounds for the appeal. If an appeal is duly filed, the board of review shall set a time and place to give the appellant an opportunity to show cause as to why the decision of the director should be changed. Following that hearing, the board of review shall, as promptly as possible, notify the appellant and the director of its decision on the appeal. The decision shall become final unless the appellant or the director files an appeal to the courts in accordance with § 28-41-26 — § 28-41-29.