Rulings
Q1: What do this card's "if your opponent has 4 or less memory" and "if they have 4 or more" mean, exactly?
It means that the condition for "if your opponent has 4 or less memory" is fulfilled when the memory is at 1 through 10 on your side, 0, or 1 through 4 on your opponent's side at the timing when this effect activates. Similarly, the condition for "if they have 4 or more" is fulfilled when the memory is at 4 through 10 on your opponent's side at the timing when this effect activates.
Q2: If my opponent has 4 memory when this effect activates, do both the effect where 1 of my opponent's Digimon with 8000 DP or more can't attack until the end of their turn and the effect where I delete 1 of their Digimon with 6000 DP or less activate?
Yes, that's correct.
Data Sources
Lv.5 Brachiomon BT15-016 U Ultimate | Data | Plesiosaur [On Play] [When Digivolving] If your opponent has 4 or less memory, 1 of your opponent's Digimon with 8000 DP or more can't attack until the end of their turn. If they have 4 or more, delete 1 of their Digimon with 6000 DP or less. --- Inherited: [On Deletion] Return 1 of your opponent's Digimon with 7000 DP or less to the hand.
Lv.5 Brachiomon BT15-016 U Ultimate | Data | Plesiosaur [On Play] [When Digivolving] If your opponent has 4 or less memory, 1 of your opponent's Digimon with 8000 DP or more can't attack until the end of their turn. If they have 4 or more, delete 1 of their Digimon with 6000 DP or less. --- Inherited: [On Deletion] Return 1 of your opponent's Digimon with 7000 DP or less to the hand.
Lv.5 Brachiomon BT15-016 U Ultimate | Data | Plesiosaur [On Play] [When Digivolving] If your opponent has 4 or less memory, 1 of your opponent's Digimon with 8000 DP or more can't attack until the end of their turn. If they have 4 or more, delete 1 of their Digimon with 6000 DP or less. --- Inherited: [On Deletion] Return 1 of your opponent's Digimon with 7000 DP or less to the hand.
Lv.5 ブラキモン BT15-016 U 完全体 | データ種 | 首長竜型 【登場時】【進化時】メモリーが相手側の4以下なら、相手のターン終了まで、DP8000以上の相手のデジモン1体はアタックできない。メモリーが相手側の4以上なら、DP6000以下の相手のデジモン1体を消滅させる。 --- Inherited: 【消滅時】DP7000以下の相手のデジモン1体を手札に戻す。