One. If it fits the space provided. It will have double the heat capacity.

If you really meant "how many 1/8W 39 ohm resistors would be required to replace a 1/4 W 39 ohm resistor?": four. two pairs connected in series, each pair connected to the other pair in parallel

One eighth watt is LESS than 1/4 watt... therefore the 1/4 watt replacement will work ok. Just use the same value 39 ohms. If you want to know how many watts are ACTUALLY flowing in the resistor, just measure the voltage across the resistor. This will USUALLY be a DC measurement, so set your meter to DC. Use ohms law to calculate AMPS flowing through the resistor (amps equals VOLTS(across resistor) divided by the resistance of the resistor (39). ) Now you know the VOLTS across the resistor... and you know the AMPS through the resistor. to get WATTS, just multiply AMPS times VOLTS equals WATTS. ............... The reason they designed it with a 1/8th watt resistor is likely because much LESS than 1/8th watt is flowing through it. As long as you do not pass MORE than 1/8th watt then a 1/8th watt resistor will work. Also a TEN WATT resistor of 39 ohms would work, but it would cost more and would not fit into the enclosure of whatever it is you are fixing.

If you really meant "how many 1/8W 39 ohm resistors would be required to replace a 1/4 W 39 ohm resistor?": four. two pairs connected in series, each pair connected to the other pair in parallel