I do not understand the "4x4" expression.
To understand wireless capabilities of a radio chipset that is 802.11n or newer, you need to understand the shorthand often used in their technical capabilities, namely AxB:C. A represents the number of Tx radio chains are available to the device, B represents the number of Rx radio chains, and C represents the number of spatial streams. In many cases where A = B = C, the C value is omitted.
A device needs to have a number of antennas equal to the highest of either A or B to make use of its capabilities (i.e. I have seen a 3x3:3 adapter in a laptop with only two antennas and in such a case it will operate no better than a 2x2:2 device).
You can never have more spatial streams than you have either Tx or Rx radio chains (i.e. you need at least one radio chain to make use of a spatial stream). You can however have more radio chains than spatial streams, and in these cases they can provide other benefits (resistance to interference, extended range, etc).
Note: most of this section of the answer was copied from my own answer here.
According to my information, with 802.11ac the 5GHz bandwidth can be divided in channels of a selectable bandwidth (20 MHz, 40 MHz, ...). The number of available channels will depend of the selected bandwidth. By example, 12 channels of 40 MHz.
You appear to understand this correctly. The actual number of 5GHz channels available for use will vary by regulatory domain (i.e. where you are in the world).
Moreover, the speed in Mbps of a single channel depends of the channel bandwidth. By example, a 40 Mhz could reach a theorical maximum of 200 Mbps. Thus, in this case, the total WiFi band (all the 12 channels of 40 MHz) will allow 12*200 Mbps = 2400 Mbps (?).
Must I understand "4x4" as that this device can exceeded this maximum of 9600 Mbps ?
This however you do not. The data rate used will be determined by a number of factors: channel width, number of spatial streams in use, the modulation/coding used, and whether the guard interval is short or long. You can find the a number of charts containing the data rates for 802.11n (HT) and 802.11ac (VHT) in many places on the Internet, for example on this chart.
There you will see that the maximum data rate (theoretical maximum) for a 40 MHz channel for a 4x4:4 802.11ac device is actually 800 Mbps.