6 2/5xz=7 1/9

Do you mean this?

6 \frac25 \times z = 7\frac19?

An easy way to confuse you the least is to first convert these fractions into improper fractions.

\frac{32}{5} \times z = \frac{64}{9}

Then, multiply both sides by 5.

\frac{32}{5} \times z \times 5= \frac{64}{9}\times 5

32z = \frac{320}{9}

Divide both sides by 32;

\frac{32z}{32} = \frac{320}{9} \times \frac{1}{32}

z = \frac{10}{9}

Now, you may wish to conver the fraction into a proper fraction:

z = 1\frac{1}{9}

I hope it helped! :)