The phrase "apprehensive about how the" is correct and usable in written English.
It can be used when expressing concern or anxiety regarding a particular situation or outcome.
Example: "She felt apprehensive about how the project would be received by the stakeholders."
Alternatives: "worried about how the" or "concerned about how the".
We were all a bit apprehensive about how the audience would react to the onslaught of craziness – and whether we were ready to show our work to the public.
The result delighted her; Sargent, a shrewder character, was apprehensive about how the portrait would be viewed by the conventional crowds for whom a day out at the Salon was a social fixture in the Paris calendar.
When I spoke to Baldwin, he was apprehensive about how the choir would adapt to being integrated into the movements of the other 11 dancers, and to being part of a larger work.
For the first time, Cyan directed the live action actors for Rivens scenes; the designers, including Richard Vander Wende, were apprehensive about how the characters would fit in the finished product.
He was apprehensive about how this breach of the rules would be received at the Académie, but their response to Don Procopio was initially positive, with praise for the composer's "easy and brilliant touch" and "youthful and bold style".
By all logic, Bekele, an Ethiopian, should be apprehensive about how fast he can run in the Wanamaker Mile, the blue-ribbon event of track and field's blue-ribbon indoor competition, the Millrose Games.
That is one why reason why campaigners for religious freedom are apprehensive about how much attention, if any, the new secretary of state John Kerry will pay to their cause.
Given the Bush administration's environmental record, many of the 19 scientists were apprehensive about how Kempthorne was going to respond to their report, which warned that projected climatic changes in the Arctic would lead to the probable elimination of two-thirds of the world's 20,000 to 25,000 polar bears in much of their range within 45 years.
But as he worked on the piece, he was less apprehensive about how it'd be received than he was motivated to confront a charged subject, which is the way he feels today.
