Hadith: When the Messenger of Allah (may Allah's peace and blessings be upon him) made Takbīr, he would raise his hands up to the level of his ears. When he bowed, he would raise his hands up to the level of his ears, and when he raised his head from bowing and said: "Allah hears those who praise Him," he would do the same

عن مالك بن الحويرث رضي الله عنه «أن رسول الله صلى الله عليه وسلم كان إذا كَبَّر رفع يديه حتى يُحَاذِيَ بهما أُذُنَيْه، وإذا ركَع رفع يَديه حتى يُحَاذِيَ بهما أُذُنَيْه، وإذا رفع رأسه من الركوع» فقال: «سَمع الله لِمَن حَمِده» فعل مِثل ذلك.
[صحيح] - [رواه مسلم]

Mālik ibn al-Huwayrith (may Allah be pleased with him) reported: When the Messenger of Allah (may Allah's peace and blessings be upon him) made Takbīr, he would raise his hands up to the level of his ears. When he bowed, he would raise his hands up to the level of his ears, and when he raised his head from bowing and said: "Allah hears those who praise Him," he would do the same.
[Authentic hadith] - [Narrated by Muslim]

Explanation

Mālik ibn al-Huwayrith informs us that when the Prophet (may Allah's peace and blessings be upon him) made Takbīr, he would raise his hands up to the level of his ears, i.e. when he made the opening Takbīr, he would raise his hands until they were on the same level with his ears. Another narration reads: “up to the level of the highest part of his ears." The Hadīth of Ibn ‘Umar (may Allah be pleased with him) reads: "He used to raise his hands up to the level of his shoulders." These are three narrations: 1. He raised his hands until they were on the same level with his ears. 2. He raised his hands until they were on the same level with the highest part of his ears. 3. He raised his hands until they were on the same level with his shoulders. One is free to choose one of these options, or he may raise his hands up to the level of his shoulders, such that the tips of his fingers are on the same level with the highest part of his ears, his thumbs with his earlobes, and his palms with his shoulders. "When the Messenger of Allah (may Allah's peace and blessings be upon him) made Takbīr, he would raise his hands," i.e. he would raise them while saying "Allah is the Greatest". One of Muslim’s narrations reads: "He raised his hands then said 'Allah is the Greatest,'" i.e. he made Takbīr after raising his hands. In another narration: "He said 'Allah is the Greatest' then raised his hands." These are three manners of raising the hands at the opening Takbīr. This act of Sunnah was reported to be done in various ways, so one should apply all of them in compliance with the Sunnah. "When he bowed, he would raise his hands up to the level of his ears," i.e. as he began to bow, he raised his hand until they were on the same level with his ears, and this is the second position in which it is recommended to raise the hands. "When he raised his head from bowing and said: 'Allah hears those who praise Him,'" i.e. when he began to raise his head from bowing, he would say "Allah hears those who praise Him," and this Dhikr is one of the duties of the prayer. "He would do the same," i.e. the Messenger of Allah (may Allah's peace and blessings be upon him) would do the same as he did when he said “Allah is the Greatest”: raised his hands until they were on the same level with his ears, and this is the third position in which it is recommended to raise the hands in prayer. These are three positions in which it is recommended to raise the hands in prayer, and the fourth is to raise the hands when standing after saying the first Tashahhud in the three-Rak‘ah and four-Rak‘ah prayers.