This is simpler than you realize.

The parametric function is linear, which means it describes a straight line, and thus is its own constant tangent.

The unit normal vector is orthogonal or perpendicular to the tangent, so to find that, simply find the negative reciprocal of the tangent slope.

The slope of the function is y/x or 6/1 = 6

The slope of the normal vector is -1/6 meaning a vector of <-6, 1> or <6, -1>

The unit normal vector is this vector divided by its magnitude.

d = √(x^2 + y^2) = √(-6^2 + 1^2) = √(36 + 1) = √37

1/√37 * <-6, 1> =

<-6/√37 , 1/√37>

the value at t = 2 is irrelevant since this is a linear function, and all values of t will have the same slope and unit normal.