Historical Linguistics and Language Families 4, Exercise 2: laryngeals

It is internal reconstruction because Saussure proposed it in 1879 from
irregularities inside the Proto-Indo-European sound system itself, without
direct evidence of the hypothetical sounds. The source says the theory
explains PIE irregularities as effects of hypothetical sounds, and that it was
based only on internal reconstruction.

Hittite mattered because Jerzy Kuryłowicz found consonantal reflexes of
these sounds in Hittite. That gave the theory evidence from an attested
language, and it then gained general acceptance. (Wikipedia, Proto-Indo-European
language.)

The source does not say more about how Hittite was used, so this solution
stops there.