Step 1: What power means.
Power tells us how fast work is done. If a machine does work $W$ in time $t$, then $P = \dfrac{W}{t}$. Here $P = 15$ W and $t = 6$ s.
Step 2: Work as force times displacement.
Work is also $W = \vec{F}\cdot\vec{S}$. The body is lifted only along the x-axis, so $\vec{S} = X\hat{i}$.
Step 3: Take the dot product.
Only the x-part of the force does work along $\hat{i}$: \[ W = (3\hat{i} + 5\hat{j} + 6\hat{k})\cdot(X\hat{i}) = 3X\ \text{J}. \] The 5 and 6 components are sideways to the motion, so they do no work.
Step 4: Find the total work.
In 6 seconds the machine does $W = Pt = 15 \times 6 = 90$ J.
Step 5: Solve for X.
$3X = 90 \Rightarrow X = 30$ m.
Step 6: Conclusion.
The body is lifted 30 m along the x-axis. \[ \boxed{X = 30\ \text{m}} \]