The Musaf prayer, which we recite on Shabbat, Rosh Hodesh and Yom Tob, may be recited early in the morning, immediately after Shaharit, and indeed it is generally recited during the morning hours upon the conclusion of the Shaharit service. However, if one did not, for whatever reason, pray Musaf in the morning, he may recite this prayer in the afternoon.
In a case where one recites Musaf in the afternoon, the question arises as to whether he should recite Musaf before or after the Minha prayer. The time for Minha begins at 6.5 Halachic hours into the day. If a person did not recite Musaf before that time, he now has two prayers to recite – Musaf and Minha. This can at times occur on Rosh Hashanah, in congregations that prolong the Shaharit service and have appeals or a long sermon before Musaf. Or, it could happen that a person sleeps late or does not feel well and so does not recite Musaf in the morning. Seemingly, the Minha prayer should be recited first, in light of the famous principle of "Tadir Ve’she’eno Tadir Tadir Kodem" – meaning, the more frequent of the two Misvot takes precedence. Since Minha is recited more frequently than Musaf, it would appear that one should first recite Minha and only then recite Musaf.
In truth, however, as the Shulhan Aruch writes, the Halacha in this case differentiates between private and congregational prayer. In the synagogue, the Musaf prayer is always recited before Minha. If a congregation were to recite Minha before Musaf, they may be misled to believe that Minha should always precede Musaf, and will then recite Minha before Musaf even before the earliest time for Minha. To avoid this potential misunderstanding, the Rabbis enacted that synagogues should always pray Musaf before Minha, even in a case where the congregation did not recite Musaf before the earliest time for Minha. Even though Minha is recited more frequently, precedence is given to Musaf out of concern for misunderstandings of this nature.
However, when a person prays privately in his home, such as an ill patient who did not recite Musaf in the morning and wishes to pray in the afternoon, then he should, indeed, recite Minha before Musaf, in accordance with the rule of "Tadir Ve’she’eno Tadir." Since he prays as an individual, there is no concern of widespread misunderstanding. However, Hacham Ben Sion Abba Shaul (Israel, 1923-1998) ruled that this applies only if one did not recite Musaf until late afternoon, in the period of "Minha Ketana." In such a case, he should indeed recite Minha before Musaf. However, if one did not recite Musaf until the period of "Minha Gedola" early in the afternoon, then he should recite Musaf first, since the preferred time for Minha begins only later, at the time of "Minha Ketana."
Summary: If a congregation did not recite Musaf until the afternoon, when the time for Minha has arrived, they nevertheless first recite Musaf and then Minha. If a person prays privately, however, and he did not recite Musaf until late afternoon, in the period of "Minha Ketana," he should first recite Minha and then Musaf. If he prays during the period of "Minha Gedola" early in the afternoon, then he recites Musaf before Minha.
