Given series:
3,4,6,7,9,10

We note:

4 is the previous term 3 increased by 1,

6 is the previous term d increased by 2,

7 is the previous term 6 increased by 1,

9 is the previous term 7 increased by 2,

10 is the previous term 9 increased by 1

We note that a term is alternately the previous term increased by 1 or increased by 2.

Since we increased by 1 to obtain the last term, we then expect the next term to be the last term 10 increased by 2 which results in 12.

10+2=12

We note:

4 is the previous term 3 increased by 1,

6 is the previous term d increased by 2,

7 is the previous term 6 increased by 1,

9 is the previous term 7 increased by 2,

10 is the previous term 9 increased by 1

We note that a term is alternately the previous term increased by 1 or increased by 2.

Since we increased by 1 to obtain the last term, we then expect the next term to be the last term 10 increased by 2 which results in 12.

10+2=12