How can a PCI-e x1 Card Host 4 Sata III Ports if One PCI-e Lane is only 4Gbps and Sata III is 6Gbps?

Unfortunately, they are playing a game others have been using, but they are not exactly lying.

The card apparently uses SATA 6 Gb/s controllers for its four ports. This means that COMMUNICATION between the card and any of its connected HDD units can happen at a maximum data transfer rate of 6 Gb/s. If you are using SATA 6Gb/s HDD units, that will happen. But then the card also has to communicate with the rest of the computer via the PCIe x1 bus. At that link the data transfer rate is less - 4 Gb/s as you say. So, using one HDD attached, the performance will not be 6 Gb/s. However, if you were using several attached HDD's, the chances are that they will not all be working at the same time. So data from unit #3, for example, may be moving over the PCIe bus while Units 1 and 2 are not using it.

I said "a game others have been using". As the best example, no mechanical HDD (that is, one with spinning disks and moving heads) can move its mechanical components fast enough to achieve 6 Gb/s data throughput. The fastest average data transfer rates reported in HDD testing (and this includes new "SATA 6 Gb/s" HDD units) come in around 150 to 200 MB/s, which means approximately 1.5 to 2.0 Gb/s. One mechanical HDD cannot even saturate the max communication capability of the previous version, SATA 3 Gb/s.

So, why is there a SATA 6Gb/s standard for the COMMUNICATION part of a SATA system? It was deliberately designed so that that communication subsystem would always be faster than other components, and hence would not limit the overall device performance. Obviously it is doing that for mechanical HDD's. In fact, the 6 Gb/s communication max is faster that what current SSD's can do, so the design concept is working for those devices.

So what the tech guys designed - and it works! - the marketing guys hyped. They are using the 6Gb/s label to sell stuff that does not actually perform that fast. In your case, OP, these things may not matter. The performance limit for one SATA mechanical HDD attached to the card you ask about is really in the HDD unit: probably less than 2 Gb/s. That is NOT limited by the communication speed limits of either the SATA controllers or the PCIe x1 bus. In fact, even with four HDD's attached to all that card's ports, you might or might not find overall performance limited by the PCIe x1 bus. It all depends on how heavily you are using those HDD units and how the load is distributed over them all.