Rewrite the following sentence to make it more concise:

The referendum was held by the government in the month of August.

The Government held a referendum in the August.

Please check my work.

If you remove "the" before "August" and use a lower-case "g" on "government", it'll be fine!

The trials were held by the allied power to bring Nazi war criminals to justice.

how do I fix the were held part

Your work is almost correct. Here's a revised version:

The government held a referendum in August.

This version is more concise while still conveying the same information.