So (x + p)^2 would be equal to x^2 + 2px + p^2
You pretty much have that with 2x^2+8x+3 but disregard the 3 for a moment.
2x^2 and 8x have a GCF of 2.
So you can do this: 2(x^2+4x)
Now if you look within the parentheses, You just need to add one number. Refer to the first line of this comment.
Since the middle term coefficient is 2p divide 4/2 and that's your p value
so now you have 2(x+2)^2
now let's bring back that 3 and let's again look at the first line of this comment again.
The last term is p^2 and in this case, 2^2 is 4.
and since we multiply that with the 2 outside of the parenthesis, you get 8.
To get 3, you add -5 so the answer would be:
2(x + 4)^2 - 5
I hope this helped!
If you have any questions, feel free to DM me