Question External GPU box for Laptop

[SinisterPebble]

Specs of External GPU Box:
Name - SPARKLE Thunderbolt™ eGPU Studio-G 750, TBX-750FA-V2

Intel Alpine Ridge Controller 1x Thunderbolt 3 Port
1 x Internal PCIe x16 slot with 4 lanes PCIe 3.0 B uilt in 750W PSU
3x PCIe 6+2 pin Power Connector 1 x Gigabyte Ethernet
2 x USB A 3.1 Gen 1 Type A (5Gbps, 7.5W) Maximum Supported GPU 346 x 170 x 77 mm
Max Power Consumption 500W
https://www.sparkle.com.tw/en/TB-Studio750

I am thinking of getting this external gpu box to go with my Asus TUF F17 FX706HC, I was wondering if it would be okay with my Laptop and which cards would be the best option for it.
also it says pcie 16x slot with 4 lanes, what does that mean?

 

[kanewolf]

Specs of External GPU Box:
Name - SPARKLE Thunderbolt™ eGPU Studio-G 750, TBX-750FA-V2

Intel Alpine Ridge Controller 1x Thunderbolt 3 Port
1 x Internal PCIe x16 slot with 4 lanes PCIe 3.0 B uilt in 750W PSU
3x PCIe 6+2 pin Power Connector 1 x Gigabyte Ethernet
2 x USB A 3.1 Gen 1 Type A (5Gbps, 7.5W) Maximum Supported GPU 346 x 170 x 77 mm
Max Power Consumption 500W
https://www.sparkle.com.tw/en/TB-Studio750

I am thinking of getting this external gpu box to go with my Asus TUF F17 FX706HC, I was wondering if it would be okay with my Laptop and which cards would be the best option for it.
also it says pcie 16x slot with 4 lanes, what does that mean?

The x16 slot with 4 lanes means that there is a physical x16 slot, but there are only x4 bandwidth.