To solve this expression, we need to first simplify the terms inside the brackets and then multiply by 1/18.

First, let's simplify (-4 + 1/5 * 2 + 1/7):
-4 + 2/5 + 1/7
To add fractions with different denominators, we need to find a common denominator, which in this case is 35.
-4 + 14/35 + 5/35
-4 + 19/35
Now, convert the mixed fraction to an improper fraction:
-4 = -140/35
Combine the fractions:
-140/35 + 19/35 = -121/35

Now, multiply the result by 1/18:
(-121/35) (1/18)
To multiply fractions, multiply the numerators together and multiply the denominators together:
(-121 1) / (35 * 18) = -121 / 630

Therefore, the final answer is -121/630.