NOAA weather forecast maps often include a valid time period, e.g: "valid from time1 thru time2." However, many maps only indicate a single time, e.g: "valid time1." In the absence of other information, does this typically (or officially) mean valid up until time1, or valid after time1?
Short answer: Valid just means the expected conditions at that certain time.
In your example the map shows a forecast of 00 hours which is valid for 0600 UTC. Basically it means that the forecast/simulation is initialized on 0600 UTC and because the forecast time is 00 hours this forecast is also valid for 0600 UTC.
NOAA also provides forecasts for several hours (or days depending on the product). In this case, your simulation may be initialized on 0600 UTC but if you want to see what the conditions on 1500 UTC are you have a forecast of 09 hours which is valid for 1500 UTC. See this example.
Since the question was referencing an aviation weather product (links no longer functional), there is a contextual answer as well. The aircraft dispatcher for an airline flight must plan the flight according to FAA regulations, some of which apply to weather information. Only specific sources of weather observations and forecast products are authorized, and the "VALID" period must also be taken into account.
If I'm planning a flight that will depart at 1400Z and arrive at 1755Z, I am not authorized to use a forecast product that was issued at 00Z and is valid at 1800Z. Even though this forecast product was issued prior to me starting to plan the flight, and thus is possibly the "most recently published product available", the product was produced for a specific valid period - namely, from 1800Z onward. I would have to reference as different product that was "valid" during my scheduled flight window.