Three facts drive this case: HBsAg is positive, the man has no symptoms, and his liver enzymes are completely normal, with nothing else turning up on serology. The question is which phase of hepatitis B that profile names.
Think of HBsAg as proof the virus is in the body and the transaminases as the gauge of liver injury. When the surface antigen lingers but the enzymes stay flat and the patient feels fine, the virus is being tolerated without ongoing hepatocyte destruction. That quiet state is the $inactive$ $carrier$ phase.
Now eliminate the rest. Acute hepatitis B would announce itself with malaise or jaundice and sharply raised enzymes plus IgM anti-HBc, which the stem rules out by calling the serology unremarkable. Chronic hepatitis B implies continuing inflammation, so it would push the ALT and AST up; normal enzymes argue against it. An active carrier likewise means replication with liver damage, again inconsistent with normal enzymes.
The only description that matches a well patient who carries the surface antigen yet has a calm, undamaged liver is the inactive carrier.
\[\boxed{\text{Inactive HBV carrier}}\]