Simplify

[ (6d) / (14fg) ] / [ (18d) / (21gx) ]

To divide by a fraction, multiply by the reciprocal:

[ (6d) / (14fg) ]  x [ (21gx) / (18d) ]

Now, multiply numerator times numerator and put that answer in the numerator; then multiply the denominator times denominator and put that answer in the denominator:

[ 6d x 21gx ] / [ 14fg x 18d ]

[ 126 dgx ] / [252 dfg ]

126 divides into 252 twice. The d's cancel and the g's concel.

= x / (2f)