Morgan is correct. That is the cold filament resistance. Tungsten has a positive temperature coefficient, increasing in resistance as it warms up. This morning, I took a 60W, 120v bulb, and measured its cold resistance, reading 26 ohms (not far from what you measured). Then I hooked it to a 12v battery, and measured 130 mA current, about 1.5W, for about 92 ohms. Not even close to 6W.Most significantly, the bulb barely glowed, very deep red in color, which could only be seen when all other lights in the room were extinguished, and is completely useless for any illumination.
Yes, you can hook a 40W or 60W bulb to 12v. However, in the case of a 60W, 120V bulb, you will only get 0.6W of light out, which is nearly useless.
A 60W, 120v light bulb has a filament resistance of 240 ohms. Power = voltage squared divided by resistance. 120v^2 / 240ohms = 60W. Now apply 12v. 12v^2 / 240ohms = 0.6W.
You cannot pass DC through a transformer. The voltage output is AC, but not a clean sine wave.
Can you explain how to run a 120v bulb from a 12v battery?
DC denotes direct current, having a non-zero average value. AC is alternating current, which may be pulsed or non-sinusoidal, but has a zero average value. A waveform may have AC superimposed upon a DC term, but you cannot transmit DC through a transformer, whether pulsed or not. You can simulate the circuit using LTSPICE, and see that the output waveform looks like this, which has _NO_ DC term: