When Bill de Blasio gets back from vacation next week, he’ll have his work cut out as he starts to gear up for re-election next year.

In 2013, a coalition that included African-Americans, liberal whites and union members helped elect him mayor, inspired by his platform of economic equality and racial justice. While a majority of black voters still support him, low overall approval ratings suggest it will be tough to hold that coalition together.

At least six separate investigations by federal, state and local agencies have marred de Blasio’s administration this year. For instance, U.S. Attorney Preet Bharara is investigating whether campaign contributions were given in exchange for favors.

Also, many have criticized the mayor’s “affordable housing” plan, cautioning that it won’t create much housing that is affordable to low-income New Yorkers, and that it would lead to more gentrification in some neighborhoods.

De Blasio is not the first big-city mayor to face problems of this kind, but he needs to think of ways he could restore confidence. Obviously, he must cooperate fully with all investigations and admit wrongdoing wherever appropriate, resolving to do better. He also needs to remember the voters who elected him and think about what kinds of policies could help restore their confidence.

Last week, de Blasio announced a plan that definitely represents a step in the right direction. He unveiled reforms to create a zoned system for commercial-waste pickup that seeks to reduce truck traffic and reduce its greenhouse gas emissions by 42 to 64 percent, according to a study by two city agencies, the Department of Sanitation and the Business Integrity Commission.

Advocates for the changes, including the Teamsters union, say the reforms also would improve labor conditions for the truckers and provide more incentive for recycling. The changes signal a commitment to a greener economy.

The sanitation reforms are not sexy, and unlike universal pre-K (an early policy win for the mayor), don’t lend themselves to cute photos. But initiatives like those might begin to glue the mayor’s allies back together.

Liza Featherstone lives and writes in Clinton Hill.