How is the 'iddah period (4 months and 10 days) calculated according to the Hijri calendar, taking into account the varying number of days in the months (28, 29, or 30 days)?

Your mother's 'iddah (waiting period) begins from the day her husband passed away, which is the 8th of Rajab. It is four months and ten days, according to the Almighty's saying: "And those of you who die and leave wives behind them, they (their wives) shall wait (as regards their marriage) for four months and ten days." [Al-Baqarah: 234]. This is calculated by completing three lunar months (Sha'ban, Ramadan, and Shawwal), then completing Rajab as thirty days, then adding ten days from Dhul-Qa'dah. Accordingly, the 'iddah ends on the 18th of Dhul-Qa'dah.