Questions:how many 4 ohm resistors must be connected in parallel to create an equivalent resistance of 0.5 ohm

here the equivalent resistance is  0.5 ohms the formula for resistors connected in parallel is ,

1/r_eff=1/r₁+1/r₂+1/r₃ , assuming all the resistor has same value for resistance

1/r_eff=1/r_x+1/r_x+1/r_x+1/r_x..........................

1/0.5 =1/4 * X

1/0.5= X/ 4

4* 1=0.5*X
4=0.5X

4/0.5=X
8=X

 Therefore eight  4 ohms resistors of must be connected in parallel to get 0.5