Well it should fit into your pc since low profile brackets are included with them and i guess there's even a 1650 low profile so if you find one it would be great too. However you can ask hp to confirm the gpu you trying to install.
It appears that the HP Prodesk 400 G6 uses nearly the same motherboard as the HP EliteDesk 600/800 G1, but with fewer memory slots. That likely means that the PCIE x16 slot has a 35watt power limit (as indicated under the PCIE x16 slot for that model) instead of full spec 75watts.
From what I've found when looking up this issues for the OP, is that HP support will likely tell you to go to the HP ProDesk 400 G6 SFF product Data sheet PDF, the Customer Support - Knowledge Base or the Maintenance and Service Guide (manual) PDF.
Then you should consider any of the two gpu however you have a very capable processor in your pc, and low profile pc must always be avoided unless for some other specific reason. Did you get for some specific reason?From what I've found when looking up this issues for the OP, is that HP support will likely tell you to go to the HP ProDesk 400 G6 SFF product Data sheet PDF, the Customer Support - Knowledge Base or the Maintenance and Service Guide (manual) PDF.
https://www8.hp.com/h20195/v2/GetPDF.aspx/4AA7-5819ENUC.pdf
http://h10032.www1.hp.com/ctg/Manual/c06513590HP ProDesk 400 G6 Small Form Factor Business PC Specifications | HP® Customer Support
Specifications page for HP ProDesk 400 G6 Small Form Factor Business PC Specifications.support.hp.com
The power supply is only 180watt, and the PCIE x16 slot likely only supplies 35watts. So a GTX 1050TI or 1650 are not an option. The GT 1030 GDDR5 version is the safest option that will work within spec. The AMD Radeon RX550X 4GB LP is also an option as it's listed on the documents and the card uses around 40-45watts, so the PCIE x16 slot might be 45-50watt capable.
Thing is Jeffrey, I asked my dad for a gaming capable pc, however the certain model did not arrive and he got me a business PC, which is the HP Prodesk g6 400 SFF. I'm apparently restricted to put these kind of cards (1050ti and so on) by space available in the case and the wattage. I've checked and I can only fit a graphics card in this pc if it's similar to these dimensions (14.58 x 3.53 x 11.13 cm). Check the image attached also.
Understood buddy what I'll say is get the 1050ti then, i checked for many 1650s single slot which don't fit the dimension you said, low-profile 1650s also same issue also if you can I'll still suggest you to visit a store and or maybe later build a system with that cpu which is very capable
A single slot low profile card like a GT 1030 is your only option for your SFF case and PCIE x16 slot position. You can only use a dual slot card if you remove the PSU from the case. Here is one option for a GT 1030 https://www.amazon.com/GIGABYTE-GeForce-GV-N1030D5-2GL-Computer-Graphics/dp/B071DY2VJR
This doesn't help the OP at all. Look at the pictures of their computer. The GTX 1650 low profile physically will not fit the case. The case only has two expansion slots and the top slot is where the PCIE x1 card would go, so you can only physically fit a single slot x16 length card in the case.
No i dint do it for the 1650, but he spoke about all the gpu like 1030,1050/ti and i guess LP rx560 not alot but you get an idea atleast.
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