Q$13.$ OABC is a trapezium.

Vector $OA=a,$ Vector $AB=b,$ Vector $OC=3b.$

$D$ is the point on $OB$ such that $OD$:$DB=4$:$5$

$E$ is the point on $BC$ such that $BE$:$EC=2$:$6$

Work out the vector DE in terms of a and $b.$

Give your answer in its simplest form.