Question

12ds/w = cd (solve for w)?

Answer 1

Write the problem:               12ds/w = cd

Divide each side by  'd':        12s/w = c

Multiply each side by  'w' :    12s = cw

Divide each side by  'c' :       12s/c = w

Was that too fast for you ?

Answer 2

$12ds/w = cd\\\\ \frac{\big{12\cdot d\cdot s}}{\big{w}} =c\cdot d\ /\cdot w\\\\\frac{\big{12\cdot d\cdot s\cdot w}}{\big{w}} =c\cdot d\cdot w\\\\12\cdot d\cdot s=c\cdot d\cdot w\ /:(c\cdot d)\\\\\frac{\big{12\cdot d\cdot s}}{\big{c\cdot d}} =\frac{\big{c\cdot d\cdot w}}{\big{c\cdot d}} \\\\\frac{\big{12 s}}{\big{c}} =w$