As per the Skanda Purana published by Gitapress Gorakpur, the killing of Tārakāsura comes in Chapter 15 under the Kēdārakhaṇḍa, under the Mahēśwara khaṇḍa. But this version does not mention about Surapadma and Simhavaktra. This version of the Skanda Purana is divided on the basis of Khandas.
The birth and anointment of Skanda have been narrated in greater detail in the Kumārakhaṇḍa
in the Rudrasaṃhitā of the The Shiva Purana.
However, there is another part of the Skanda Purana (based on southern manuscripts) divided on the basis of 6 samhitas
(each samhita contains khandas, instead of being directly divided on the basis of Khandas, which has not been included by Gitapress) which would be talking about Surapadma and Simhavaktra and upon which the Tamil Kanda Puranam is based.
I don’t know in which chapter in the Samhita version they’re mentioned and where this version is available, it is however said that the Tamil Kanda Puranam is based on the Shivarahasya Khanda of the Shankara Samhita of the Skanda Purana.
Gitapress seems to be selling the Samhitas separately and as per the index of the Sūta Samhita Mimamsa sold by them, the Maheshwara Khanda seems to form part of the Sūta samhita.