Fan-out of TTL inverter
The value for fanout is the lower number of high-output or low output cases.

For traditional TTL gates such as 7400 the output low current is specified as 16mA for 0.8V Vol.

The input low current is 1.6ma giving a fanout of 10 for this case.

For the output high case the output capability that could maintain 2.4V is specified as 0.4mA.  The worst case input current in the high state is 40uA giving a fanout of 10 in this case as well.

I've never seen a device where the Voh could not be maintained so I suspect the specifications were juggled a bit to make the output low and output low cases match.

Be aware that when you connect the inputs of a gate together the currents may not multiply depending upon the specific device.

For example if you connect the two inputs of a single gate within a 7400 two input NAND together, the input low current is still only 0.4mA and the input high current is still only 40uA because the inputs go to the same transistor.  Whereas for a 7402 2 input NOR gate the inputs go to separate transistors so they multiply by 2 to 0.8mA and 80uA respectively.