\(\left|\overrightarrow{{F}}_{{q}}\right|=\frac{2 {k} \lambda}{{r}} \cdot {q}\)

\(\left|\vec{F}_{-q}\right|=\frac{2 k \lambda}{r+x} \cdot q\)

\(\Rightarrow \quad\left|\vec{F}_{\text {net }}\right|=\frac{2 k \lambda q}{r}-\frac{2 k \lambda q}{r+x}\)

\(\left|\vec{F}_{n e t}\right|=\frac{2 k \lambda q \cdot x}{r(r+x)}\)

\(4=\frac{2 \times 9 \times 10^{9} \times 3 \times 10^{-6} \times q \times 2\, m m}{10 \,m m .12 \,m m}\)

\(\Rightarrow \quad q=4.44\, \mu C\)