The correct increasing order of trans-effect of the following species is:

The trans-effect is the ability of a coordinated ligand to direct the substitution of the ligand occupying the position trans (opposite) to itself. The intensity of the trans-effect follows an empirical series.

1. General Order: Strong $\pi$-acceptors > Strong $\sigma$-donors > Weak $\pi$-donors/Weak $\sigma$-donors.
2. Specific Ligands:

• $CN^-$ (Cyanide): A very strong trans-directing ligand due to strong $\sigma$-bonding and $\pi$-backbonding capabilities. It is at the high end of the series.
• $C_6H_5^-$ (Phenyl): A strong $\sigma$-donor ligand, typically placed higher than halides but lower than cyanide.
• $Br^-$ (Bromide): A halide, acts as a weak to moderate trans-director. Its effect is less than that of $CN^-$ or $C_6H_5^-$ but greater than neutral amines.
• $NH_3$ (Ammonia): A neutral ligand with no $\pi$-bonding capability, acting as a relatively weak trans-director.

3. Conclusion: The decreasing order of trans-effect is: $CN^- > C_6H_5^- > Br^- > NH_3$. (Note: Although the question asks for 'increasing' order, the options use the '>' symbol, indicating a decreasing sequence from left to right, which matches the standard series).