Force experienced by the proton is

$\overrightarrow {\text{F}}  = {\text{q}}(\overrightarrow {\text{v}}  \times \overrightarrow {\text{B}} ) = {\text{q}}(3\widehat {\text{i}} + 2\widehat {\text{j}}) \times (2\widehat {\text{j}} + 3\widehat {\text{k}})$

$ = q(6\hat i - 9\hat j + 6\hat k)$

$ = 3{\text{q}}(2\widehat {\text{i}} - 3\widehat {\text{j}} + 2{\text{k}})\,{\text{N}}$

Acceleration $ = \frac{{\text{F}}}{{\text{m}}} = \frac{{3{\text{q}}}}{{\text{m}}}(2{\text{i}} - 3{\text{j}} + 2{\text{k}})$

$ = 3 \times \left( {0.96 \times {{10}^8}} \right)(2i - 3j + 2k)$

$ = 2.88 \times {10^8}(2\widehat {\text{i}} - 3\widehat {\text{j}} + 2{\text{k}}){\mkern 1mu} {\text{m}}{{\text{s}}^{ - 2}}$

Hence the correct choice is $( 2)$