A. Signing the Payne-Aldrich tariff
Let's look at the available options and see what their effects were.
A.Signing the Payne-Aldrich tariff.
* The Payne-Aldrich tariff was a compromise bill that frustrated both proponents and opponents of reducing tariffs. After Taft signed the bill, the Republican Party split into Progressives and Old Guards. This split cost the Republican's the 1910 congressional election. This is the correct choice.
B.Busting 90 trusts in a four-year term.
* President Taft was even more aggressive than President Roosevelt was in anti-trust suits. So you could consider this a continuation of a policy previously established by the Republican party and this didn't anger the progressives in that party. So this is a wrong answer.
C.Dismissing James Sherman as his vice president.
* President Taft didn't dismiss Vice President Sherman. James Sherman died October 30, 1912. So this is also a wrong choice.
D.Appointing Gifford Pinchot as Secretary of Interior.
* Since Gifford Pinchot was never the Secretary of Interior (Richard A. Ballinger was secretary from 1909–1911 and Walter L. Fisher from 1912-1913), this can't be the reason. So this too is a bad choice.