The Orthodox Study Bible, published by the St. Athanasius Academy of Orthodox Theology, in its comment on Mark 13:32, reads:
The Orthodox Study Bible - Mark 13:32
Though Jesus declares that the Son does not know the day of His own return, St. John Chrysostom teaches that this is not to be understood literally, but as a figure of speech. The meaning is simply that Christ will not reveal the exact day to anyone, and that believers should not be so brazen as to inquire of Him.
Above, the Orthodox Study Bible takes the traditional interpretation of Mark 13:32 (and its parallel in Matthew 24:36), which is that Jesus actually did know the day and hour of His return.
The verse in question is part of a passage, which in part reads:
Mark 13:32-37
32 But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.
33 Take ye heed, watch and pray: for ye know not when the time is.
34 For the Son of man is as a man taking a far journey, who left his house, and gave authority to his servants, and to every man his work, and commanded the porter to watch.
35 Watch ye therefore: for ye know not when the master of the house cometh, at even, or at midnight, or at the cockcrowing, or in the morning:
36 Lest coming suddenly he find you sleeping.
37 And what I say unto you I say unto all, Watch.
Note that this passage is Jesus's response to His disciples asking, "Tell us, when will these things be? What is the sign that these things are all about to be fulfilled?" (Mark 13:4), referring to the events of the last days. And, in response, Jesus clearly says that He does not know the day and hour of these events, which culminate in His second coming (Mark 13:26), but rather, only the Father knows.
For classical commentators, this presented a problem, as if Jesus is fully God, then He has the divine mind, and therefore, is omniscient. If Jesus were not omniscient, despite being "fully God", then that would seem to divorce omniscience from the divine Essence. And, in that case, Jesus would not have omniscience, but the Father and Spirit would, yet, all are supposed to be the same Being. Therefore, the idea that Jesus did not actually know the day and hour of His second coming was rejected by the classical commentators.
But, notice how Jesus speaks in the passage. In verse 32, He uses the same instance of the word "know", and applies it to people in general, then angels, then Himself. In context, the people in general clearly do not "know" in the sense that they "lack knowledge of" when the event will take place, which is why Jesus goes on to tell them to be on watch - "Take ye heed, watch and pray: for ye know not when the time is" (Mark 13:33). There is nothing in the context of the preceding verse to suggest that, although Jesus meant not "know" in the sense of "lack knowledge of" when referring to men and angels, He, without so much as repeating the word, meant not "know" in the sense of "did have knowledge of, but chose not to declare", or "did not know in only part of Himself".
Consider the perspective of those listening to Jesus speak. They are asking Him a question, essentially, "When are these things going to happen?". And, in response, He finally says that no one knows - not men, not angels, not Himself - only the Father knows. This would have been relatively straightforward to them. Would any of them, from such a response, have gathered that He actually did know? In order to come to that conclusion, they would need to conclude the exact opposite of what He has just told them.
And, notice that Jesus explicitly marks out the Father as having this knowledge, in distinction from Himself. The account in Matthew even contains the word "only", saying "but my Father only" (Matthew 24:36). If the "Father only" has this knowledge, and Jesus explicitly says that the Son does not have it, then the conclusion that Jesus did, in spite of this, actually know the day and hour, comes from reading a pre-conceived theology into the passage, and not the context of the passage itself.
The Orthodox Study Bible continues the tradition of classical Trinitarian thought with regard to Mark 13:32, which attempts to teach what is the opposite of what Jesus confessed in the passage, which was that He did not have knowledge of the day and the hour of His second coming, and that rather, only the Father had such knowledge. This passage, however, in spite of such interpretations, demonstrates to a student of Scripture that Jesus is distinct from God, and is not God.