When dealing with the state budget, the governor of Texas has this power, allowing for the selective veto of specific budget items.?

the line item veto

Explanation:

The line item veto allows the Texas governor to veto specific items in an appropriation bill without killing the entire bill. The state budget is an appropriation bill, so the governor can veto specific budget items.

The bill itself is submitted by the governor, but the state legislature must approve it, and it can also change it.