# Can two 2p orbitals of an atom hybridize to give two hybridized orbitals?

No. They are the same in energy, so it would lose the point to hybridize them. They have no necessity to hybridize with other $2 p$ orbitals.
As a result, if you attempt to hybridize two different $2 p$ orbitals, it will not work. There is no energy benefit.
On the other hand, a $2 s$ can hybridize with some $2 p$ orbitals to form $s p$, $s {p}^{2}$, or $s {p}^{3}$ hybridizations depending on how many $2 p$ orbitals hybridize.
Since methane must make four identical $\text{C"-"H}$ bonds, it must use four identical orbitals, so it hybridizes one $2 s$ with all three $2 p$ orbitals to form four $s {p}^{3}$ hybrid orbitals, one for each $\text{C"-"H}$ $\sigma$ bond.
All four of these $\setminus m a t h b f \left(s {p}^{3}\right)$ orbitals are lower in energy than the original $\setminus m a t h b f \left(2 p\right)$ orbitals.