Identify strongest base from following.

Base strength in aqueous solution depends on the balance between inductive effects, steric hindrance, and solvation stability.

Alkyl groups donate electron density through the $+I$ effect, increasing nitrogen's basicity. However, larger alkyl groups introduce steric hindrance and reduce conjugate acid solvation through hydrogen bonding.

For methyl-substituted amines: $(\mathrm{CH}_3)_2\mathrm{NH}$ provides optimal balance with strong inductive effect from two methyl groups, moderate steric hindrance, and adequate solvation of its conjugate acid $(\mathrm{CH}_3)_2\mathrm{NH}_2^+$ which forms two hydrogen bonds.

$\mathrm{CH}_3\mathrm{NH}_2$ has weaker inductive effect and $\mathrm{NH}_3$ has no alkyl groups, while $(\mathrm{CH}_3)_3\mathrm{N}$ suffers from significant steric hindrance and poor solvation of its conjugate acid.

The basicity order is secondary $>$ primary $>$ tertiary $>$ ammonia, making $(\mathrm{CH}_3)_2\mathrm{NH}$ the strongest base.