What does the Greek word for 'counted' mean in Romans 4?

In Romans 4, the Greek word for 'counted' is a bookkeeping term meaning 'imputed' or 'put to the account.' It conveys crediting something to someone's account. This same word appears in many other places in Romans with that same accounting sense.

Les teaches that the word 'counted' in Romans 4 comes from a Greek term that was a bookkeeping term. He says it is used in many other places in Romans as 'imputed' or 'put to the account.' To illustrate, Les directs us to the little book of Philemon, just ahead of Hebrews, where the same identical word is used in a setting that is easy to understand. There, a slave had run away from his owner, became a believer through Paul's gospel, and Paul pleads for him to be accepted back without punishment, as an obedient believer should return to his master.

Romans 4:5

But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.

What kind of believing is counted in God's accounting?

The believing that is counted is faith in the one who justifies the ungodly. It is not working but trusting Him who justifies the ungodly. That kind of believing is counted, imputed, or put to the account, a Greek bookkeeping term used in Romans.