Question

how many solutions are there in this equation 8 (x-3)=8x-24

Answer 1

Performing the indicated multiplication on the left side gives you:

8x-24=8x-24,

8x=8x

1=1 

These expressions are true for any real value of x and thus has infinitely many solutions...

Answer 2

It should be all real numbers, because if you plug in lets say a 1 that would be 8(1-3) = 8(1) -24  or a 2 that would be 8(2-3)= 8(2) -24
     8(-2) = 8 -24                                          8(-1) = 16 -24
      -16  = -16                                               -8    =    -8