To make sure the 12-page U.S. emergency passport is accepted for entry, you should check entry requirements of your destination: https://travel.state.gov/content/travel/en/international-travel/International-Travel-Country-Information-Pages.html.
Some countries will only permit direct transit for a destination in the United States with an emergency passport.

If your passport is lost, stolen, or damaged, a replacement passport can be issued upon presentation of proof of identity and U.S. citizenship (e.g., birth certificate, driver’s license, or previous passport).  An appointment for an application for a temporary passport for immediate, emergency travel can be scheduled on the phone at +36-1-475-4164 (during working hours).  Please note that the Embassy cannot replace passports after hours or on weekends.

To replace your lost or stolen passport, you will need:

• For an adult passport, 165 USD (or HUF equivalent), and for a minor passport, 135 USD (or HUF equivalent). Payment can be made in cash or by credit card.
• Form DS-11: Application for a U.S. Passport
• Form DS-64: Statement Regarding a Lost or Stolen U.S. Passport Book And/Or Card
• One 5 cm x 5 cm (or 2″x 2″) photo with a light background. Please, take off your eyeglasses for your photo.
• For a stolen passport, the police report documenting the theft
• All applicants issued a Social Security Number, including children under 16, must provide it on their passport application forms in accordance with 22 U.S.C. 2741a and 22 C.F.R. 51.60(f).

To replace your damaged passport, you will need:

• For an adult passport, 165 USD (or HUF equivalent), and for a minor passport, 135 USD (or HUF equivalent). Payment can be made in cash or by credit card.
• Form DS-11: Application for a U.S. Passport
• One 5 cm x 5 cm (or 2″x 2″) photo with a light background. Please, take off your eyeglasses for your photo.
• A sworn statement (to be signed ONLY in the presence of a consular officer) detailing the nature of the damage and the circumstances under which the damage took place
• All applicants issued a Social Security Number, including children under 16, must provide it on their passport application forms in accordance with 22 U.S.C. 2741a and 22 C.F.R. 51.60(f).