Summary: - Yes, Muruga did take on the position of a guru for Lord Shiva and did explain him the meaning of the Pranava, though the 2 crore verse thing hasn’t been mentioned.
Detailed
This story has been described in the Skanda Purana Śaṁkara Saṁhitā, Śivarahasya khaṇḍa, Sambhava kāṇḍa
Per say it wasn’t that Brahmaji was a guru to Skanda. It was due to Brahmaji’s arrogance about his knowledge, that Skanda asked him for the meaning of pranava. In arrogance, he gave the meaning as himself, which angered Skanda and he put him in jail. The devatas then go to Chandramauliswara Bhagavan for help, on being asked by whom, Skanda briefly describes what happened:
अनादृत्य तु मां दर्पाद्यातायातं चकार सः। मया पृष्टः ततः कस्त्वं कृत्यं ते किं क्व वा स्थितिः। किमधीतं त्वया ब्रूहीत्यधिक्षेपः कृतो मया॥ न्यवेदयत्तो मह्यं स्वंच कृत्यं च कौशलम्। वैदुष्यमात्मनश्चापि विद्यास्वष्टदशस्वपि॥ पुनः पृष्टश्चवेदानां स्वरमाद्यं च तस्य च। अर्थश्चानेन यत्किंचिदन्यथार्थोऽनुवर्णितः॥ ततोऽन्यथार्थवक्तारं प्रणवस्य महामनोः। न्यवेशयमहं काराग्रहमध्यं प्रजापतिम्॥
While entering and exiting he (Brahma) insulted me. On being taunted by me, “who are you, what are your deeds, your position and what have you studied?”, he told me everything about his deeds and excellence, his being knowledgeable in the eighteen kinds of vidyas. On being asked again about the beginning letter of the Vedas, the meaning of it was described something other than the true meaning. I thus put Prajapati, who was the speaker of a wrong meaning of the pranava in jail.
-Chapter 34, verses 17-21
Chandralalama Bhagavan is very happy with his son and asks him to explain the meaning of Pranava. Skanda advises for the appearance of a guru, because a mantra should be given by a guru and should be carefully protected, rather than being spoken in public.
ततः प्रीतमनाः शंभुः पुत्रमाघ्राय गण्डयोः। पप्रच्छाग्रे मनोरर्थे देवानामात्मसम्भवम्॥ प्रोवाच पुनः स्कन्दः प्रणिपत्य जगद्गुरुम्। रहस्यभूतमत्यर्थमर्थमग्रे कथं पितः॥ कथयानि च देवानामग्रे विश्वजगद्गुरोः। गुरुं प्रकटयेद्धीमान् मन्त्रं यत्नेन गोपयेत्॥
Then being happy, Shambhu kissed his son on his cheeks and in front of the devatas asked him for the meaning of the Pranava. Skanda then bowed to the guru of the world and said that one whose meaning is a secret, how can I say it in front of the devatas and in front of the guru of the world? Therefore a smart person should create a guru and the mantra should be protected with care.
-Chapter 34 verses 22-24
Bhagavan Shri Dakshinamurti then performs the necessary action of making Skanda a guru and allowing him to speak the meaning of Om in his ears, like a guru:
गदन्तमिति तं पुत्रं मुहुराघ्राय मूर्धनि। अङ्के निधाय चालिङ्ग्य कर्णे कथय पुत्रक॥ ममेति व्याहरत्पुत्रं मन्त्रार्थमिति सस्पृहम्। ततोऽभिवाद्य मनसा पितरं परया मुदा॥ अर्थमाहस्य सेनानीः प्रणवस्य रहस्यथ।
While his son was speaking in such a manner, Lord Shiva kissed him again, picked him in his lap and while hugging him, with desire, told him, “Speak the meaning of the mantra in my ear.” Then saluting his father with extreme joy, Senani spoke the meaning of the Pranava in secret.
-Chapter 34 verses 26-28
So, yes Lord Muruga did become Guru to Lord Shiva and gave the complete explanation of OM
The two crore verse thing hasn’t been mentioned, but in short, the meaning of the Pranava as given by Skanda is:
सुब्रह्मण्यों स्वरस्यार्थस्त्वं चाहं च सदाशिवोम्।
The meaning of the syllable is Subrahmanya (the lord who is ever compassionate to the Brahmins), you (indicative of the Mahavakya - tattvamasi), me (indicating the Mahavakya Aham Brahmasmi) and Sadashiva (the lord who is eternally auspicious).
-Chapter 34, verse 29
One thing must be understood is that Lord Parvati Pati is Jagadguru, charachara guru, which has been acknowledged by Skanda above. Yet accepting another as his guru was his way of getting the Pranava to be revealed. He subsequently instructs Skanda to give the mantrartha to Agastya muni and start a parampara.
