To solve this equation, we can first simplify the left side by finding a common denominator for 19 and 6.

7/19z - 1/6 = 1/16

To find a common denominator for 19 and 6, we multiply them together:
19 * 6 = 114

Now we can rewrite the equation with the common denominator:
(7/19z 6/6) - (1/6 19/19) = 1/16
(42/114z - 19/114) = 1/16

Now we can combine the fractions on the left side:
(42 - 19)/114z = 1/16
23/114z = 1/16

To solve for z, we can cross multiply:
23 * 16 = 114z
368 = 114z

Finally, we can solve for z by dividing both sides by 114:
368/114 = z
z = 3.23

Therefore, z = 3.23.