Let $F(t)=cos(2t)i+3tj+t^{4}k$ and $G(t)=t^{6}cos(2t)i+t^{4}j+2e^{6t}k,$ find $F(t)*G(t).$

$A.(6t{e}^{6t}-t^8)i+(t^{10}-2e^{6t})cos(2t)j+(t^4-3t^7)cos(2t)k$

$B.(t^{6}co{s}^2(2t)+3t^5+2t^4{e}^{6t})j$

$C.t^{6}co{s}^2(2t)+3t^5+2t^4{e}^{6t}$

$D.6t{e}^{6t}-t^8+(t^{10}-2e^{6t})cos(2t)+(t^4-3t^7)cos(2t)$

$E.t^{6}co{s}^2(2t)i+3t^{5}j+2t^4{e}^{6t}k$