The "this" in the above quote referred to people hardening their own hearts through the practice of sin. I included Romans 9:18 to provide a complete list of the word usage, although the verse is non-germane because it refers to being hardened by God rather than us hardening ourselves by the practice of sin.
Act 19:9
But when some were
becoming hardened and disobedient, speaking evil of the Way before the people, he withdrew from them and took away the disciples, reasoning daily in the school of Tyrannus.
Romans 9:18
So then He has mercy on whom He desires, and He
hardens whom He desires.
Hebrews 3:8
DO NOT
HARDEN YOUR HEARTS AS WHEN THEY PROVOKED ME,
AS IN THE DAY OF TRIAL IN THE WILDERNESS,
Hebrews
3:13
But encourage one another day after day, as long as it is
still called “Today,” so that none of you will be
hardened by the deceitfulness of sin.
Hebrews 3:15
while it is said,
“TODAY IF YOU HEAR HIS VOICE,
DO NOT
HARDEN YOUR HEARTS, AS WHEN THEY PROVOKED ME.”
Hebrews
4:7
He again fixes a certain day, “Today,” saying through David after so long a time just as has been said before,
“TODAY IF YOU HEAR HIS VOICE,
DO NOT
HARDEN YOUR HEARTS.”