Can an extruder rated for 24 V work with 12 V ATX power supply?
Electrical engineering can be quite complex, but in this case you can save yourself with same simple equations/relations. Using the following formulae:


Voltage ($\ U$) equals current ($I$) multiplied by the electrical resistance ($R$)


$$ U=I \times R $$ 

and 


Power ($P$) equals the square of the current multiplied by the electrical resistance


$$ P=I^2 \times R $$
can be rewritten using the first formula to:
$$ P= \frac{U^2}{R} $$

Applying these formulae to a 40&nbsp;Watt, 24&nbsp;V heater element, the electrical resistance (in $\Omega $) is calculated by:
$$ \frac{{(24\ V)}^2}{40\ W}=14.4\ \Omega $$

Running this heater element with 12&nbsp;V will lead to a power of 
$$ \frac{{(12\ V)}^2}{14.4\ \Omega}=10\ W $$ 

The heat produced is proportional to the square of the current multiplied by the electrical resistance, halving the voltage is quartering the heat output. This will heat up very slowly! If it is able to reach the required temperature that is. Calculating the temperature is far more difficult, but if you are interested in doing so, please look into this answer from the Electrical Engineering Stack Exchange.