To rest, in Hebrew, is the simple verb לנוח

. 

To place something down – to cause it to rest – is the הפעיל verb להניח

, as in:

אתה יכול להניח את הפרחים על השולחן.

You (a male) can put the flower down on the table.

We can place down not only physical objects, but also ideas, positioning them as the foundation for other ideas. In English we call this to assume. In Hebrew it’s להניח

, while הנחה

is assumption (also a discount – putting down the price of something).

For example:

בהנחה שהיא צודקת, אנחנו בבעיה.

Assuming (under the assumption) that she’s right, we have a problem (we’re in a problem).